Ever wondered how to work out square roots without a... Show more
Maths206 views·Updated Jun 1, 2026·2 pagesEstimating Square Roots Without a Calculator
Scarlett Edwardes@scarlett_1917
1
of 2
Estimating Square Roots - The Basics
When you need to estimate square roots without a calculator, you're essentially playing a clever guessing game. The key is finding the perfect square that's closest to your number.
Let's say you need to find √83. You know that 9² = 81, which is only 2 away from 83. Since 83 is just slightly bigger than 81, √83 must be just over 9 - roughly 9.1.
The method works because you're thinking about where your number sits between two perfect squares. Since the next perfect square after 81 is 100 (which is 10²), and 83 is much closer to 81, your estimate will be just slightly above 9.
Quick Tip: Always identify the perfect squares on either side of your number first - this gives you the "boundaries" for your estimate.
2
of 2
Step-by-Step Examples
Example 1: √26 First, spot that 25 (which is 5²) is the closest perfect square, just 1 away from 26. The next perfect square is 36 (6²). Since 26 is very close to 25 and far from 36, √26 ≈ 5.1.
Example 2: √110 Here, 100 (10²) is closest, being 10 away from 110. The next perfect square is 121 (11²). Notice that 110 sits roughly halfway between 100 and 121, so √110 ≈ 10.5.
The pattern is simple: if your number is close to the smaller perfect square, add a small decimal. If it's roughly in the middle, add around 0.5.
Remember: You're not aiming for perfection here - just a reasonable estimate that gets you in the right ballpark!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar content
Most popular content: Estimation
2MathsEstimating Calculations Guide
Explore effective techniques for estimating calculations in mathematics. This guide covers rounding numbers, using significant figures, and applying approximation methods through practical examples. Ideal for students looking to enhance their estimation skills in problem-solving.
93642
MathsEstimation Techniques
Explore effective estimation techniques including rounding numbers and using the bus stop method for division. This summary covers key steps in estimating sums and converting remainders into fractions, making it essential for mastering basic arithmetic skills.
71974
Most popular content in Maths
9MathsComprehensive Maths Concepts
Explore essential mathematical concepts including powers, geometry, statistics, and probability. This resource features 65 pages of detailed explanations, diagrams, and examples to enhance your understanding of topics such as right triangles, volume calculations, and data representation. Ideal for students seeking to strengthen their numeracy skills and grasp complex mathematical principles.
1079,7766,318
MathsGCSE Maths (Higher) // Revision Guide
The only GCSE maths (higher) revision guide you need to get a grade 9! Contains every topic, each with all potential question types and their solutions.
102,33054
M
MathsMedium Level alerbra
Master challenging maths concepts with this medium level flashcard set designed for grade 7/8 students. Strengthen your problem-solving skills and boost your confidence in maths!
75533
MathsComprehensive Maths Concepts
Explore essential mathematical concepts including polynomial theorems, logarithmic properties, trigonometric functions, and integration techniques. This resource covers everything from solving inequalities to understanding exponential functions, providing a solid foundation for A-level mathematics. Ideal for students aiming for top grades.
1221,9901,818
M
MathsMastering Maths: Essential Concepts for Grade 10
Boost your math skills with this comprehensive flashcard set covering key concepts for grade 10. Perfect for exam preparation and building a strong foundation in mathematics.
104261
M
MathsMastering Medium-Level Maths: Essential Flashcards for Grade 11 Students
Boost your Maths skills with this comprehensive set of flashcards designed specifically for Grade 11 students. Covering medium-level topics, these cards will help you ace your exams and build a solid foundation for advanced Maths.
118823
MathsComprehensive Maths Concepts
Explore essential higher mathematics concepts including calculus, trigonometry, polynomials, and vector analysis. This summary covers key topics such as differentiation, integration, quadratic equations, and the properties of circles, providing a solid foundation for exam preparation. Ideal for students seeking a concise yet thorough review of advanced mathematical principles.
S51,93757
P
MathsPercentage,fractions and decimals
how well do you know percentages,fractions and decimals
72703
M
Mathsmaths SOHCAHTOA
Trigonometric ratios SOHCAHTOA for calculating angles and sides in right-angled triangles.
111740
Most popular content
9
SociologySociology of Education Overview
Explore comprehensive A-Level Sociology notes on the education system, covering key theories, policies, and sociological perspectives. This resource includes insights on marketisation, gender roles, cultural deprivation, and educational inequalities, providing a thorough understanding of how education shapes social stratification and individual achievement. Ideal for exam preparation and in-depth study.
12102,3893,038
CriminologyCriminology: Crime & Punishment Overview
Comprehensive mindmaps covering key concepts in the Crime and Punishment topic for WJEC Criminology Unit 4. This resource includes detailed insights into the Criminal Justice System, crime prevention strategies, sentencing models, and the roles of various agencies. Ideal for A-Level revision, ensuring you grasp essential theories and legislative processes to excel in your exams.
1254,8131,059
SociologySociology of Families: Comprehensive Revision
Dive into an extensive overview of family dynamics, perspectives, and patterns in sociology. This resource covers key concepts such as family diversity, gender roles, marriage, and the impact of social policies on family structures. Perfect for A-Level Sociology students preparing for Paper 2.
1273,2392,304
English LiteratureAn Inspector Calls: Character Insights
Explore in-depth analysis and key quotes for characters in J.B. Priestley's 'An Inspector Calls'. This resource covers Gerald Croft, Inspector Goole, Sheila Birling, Mrs. Birling, Eric Birling, and Eva Smith, focusing on themes of class, gender roles, and social responsibility. Ideal for students aiming for Grade 8 and above.
1025,231901
CriminologyWJEC Unit 4 Criminology
Criminology unit 4 detailed revision note
127,120124
CriminologyCriminology Theories Overview
Explore key criminology theories and their implications on crime and deviance. This comprehensive summary covers biological, psychological, and sociological perspectives, including labelling theory, right realism, and the impact of social campaigns on policy development. Ideal for A-Level criminology students seeking to understand the complexities of criminal behaviour and the factors influencing crime prevention strategies.
129,746211
English LiteratureRomeo and Juliet: Key themes
Key Romeo and Juliet themes and analysed quotes
106,619197
C
BiologyCell Biology and Cell structure
cell structures
92,6740
English LiteratureMacbeth: Guilt and Ambition
Explore the complex themes of guilt and ambition in Shakespeare's 'Macbeth'. This analysis covers key characters, including Macbeth and Lady Macbeth, their moral dilemmas, and the tragic consequences of their ambition. Ideal for students studying character motivations, thematic elements, and the psychological impact of power. Includes insights on the natural order, manipulation, and the descent into madness.
918,818392
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user
Maths206 views·Updated Jun 1, 2026·2 pagesEstimating Square Roots Without a Calculator
Scarlett Edwardes@scarlett_1917
Ever wondered how to work out square roots without a calculator when the number isn't a perfect square? It's actually quite straightforward once you know the trick of finding the closest perfect squares and making smart estimates.
1
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Estimating Square Roots - The Basics
When you need to estimate square roots without a calculator, you're essentially playing a clever guessing game. The key is finding the perfect square that's closest to your number.
Let's say you need to find √83. You know that 9² = 81, which is only 2 away from 83. Since 83 is just slightly bigger than 81, √83 must be just over 9 - roughly 9.1.
The method works because you're thinking about where your number sits between two perfect squares. Since the next perfect square after 81 is 100 (which is 10²), and 83 is much closer to 81, your estimate will be just slightly above 9.
Quick Tip: Always identify the perfect squares on either side of your number first - this gives you the "boundaries" for your estimate.
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Step-by-Step Examples
Example 1: √26 First, spot that 25 (which is 5²) is the closest perfect square, just 1 away from 26. The next perfect square is 36 (6²). Since 26 is very close to 25 and far from 36, √26 ≈ 5.1.
Example 2: √110 Here, 100 (10²) is closest, being 10 away from 110. The next perfect square is 121 (11²). Notice that 110 sits roughly halfway between 100 and 121, so √110 ≈ 10.5.
The pattern is simple: if your number is close to the smaller perfect square, add a small decimal. If it's roughly in the middle, add around 0.5.
Remember: You're not aiming for perfection here - just a reasonable estimate that gets you in the right ballpark!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar content
Most popular content: Estimation
2MathsEstimating Calculations Guide
Explore effective techniques for estimating calculations in mathematics. This guide covers rounding numbers, using significant figures, and applying approximation methods through practical examples. Ideal for students looking to enhance their estimation skills in problem-solving.
93642
MathsEstimation Techniques
Explore effective estimation techniques including rounding numbers and using the bus stop method for division. This summary covers key steps in estimating sums and converting remainders into fractions, making it essential for mastering basic arithmetic skills.
71974
Most popular content in Maths
9MathsComprehensive Maths Concepts
Explore essential mathematical concepts including powers, geometry, statistics, and probability. This resource features 65 pages of detailed explanations, diagrams, and examples to enhance your understanding of topics such as right triangles, volume calculations, and data representation. Ideal for students seeking to strengthen their numeracy skills and grasp complex mathematical principles.
1079,7766,318
MathsGCSE Maths (Higher) // Revision Guide
The only GCSE maths (higher) revision guide you need to get a grade 9! Contains every topic, each with all potential question types and their solutions.
102,33054
M
MathsMedium Level alerbra
Master challenging maths concepts with this medium level flashcard set designed for grade 7/8 students. Strengthen your problem-solving skills and boost your confidence in maths!
75533
MathsComprehensive Maths Concepts
Explore essential mathematical concepts including polynomial theorems, logarithmic properties, trigonometric functions, and integration techniques. This resource covers everything from solving inequalities to understanding exponential functions, providing a solid foundation for A-level mathematics. Ideal for students aiming for top grades.
1221,9901,818
M
MathsMastering Maths: Essential Concepts for Grade 10
Boost your math skills with this comprehensive flashcard set covering key concepts for grade 10. Perfect for exam preparation and building a strong foundation in mathematics.
104261
M
MathsMastering Medium-Level Maths: Essential Flashcards for Grade 11 Students
Boost your Maths skills with this comprehensive set of flashcards designed specifically for Grade 11 students. Covering medium-level topics, these cards will help you ace your exams and build a solid foundation for advanced Maths.
118823
MathsComprehensive Maths Concepts
Explore essential higher mathematics concepts including calculus, trigonometry, polynomials, and vector analysis. This summary covers key topics such as differentiation, integration, quadratic equations, and the properties of circles, providing a solid foundation for exam preparation. Ideal for students seeking a concise yet thorough review of advanced mathematical principles.
S51,93757
P
MathsPercentage,fractions and decimals
how well do you know percentages,fractions and decimals
72703
M
Mathsmaths SOHCAHTOA
Trigonometric ratios SOHCAHTOA for calculating angles and sides in right-angled triangles.
111740
Most popular content
9SociologySociology of Education Overview
Explore comprehensive A-Level Sociology notes on the education system, covering key theories, policies, and sociological perspectives. This resource includes insights on marketisation, gender roles, cultural deprivation, and educational inequalities, providing a thorough understanding of how education shapes social stratification and individual achievement. Ideal for exam preparation and in-depth study.
12102,3893,038
CriminologyCriminology: Crime & Punishment Overview
Comprehensive mindmaps covering key concepts in the Crime and Punishment topic for WJEC Criminology Unit 4. This resource includes detailed insights into the Criminal Justice System, crime prevention strategies, sentencing models, and the roles of various agencies. Ideal for A-Level revision, ensuring you grasp essential theories and legislative processes to excel in your exams.
1254,8131,059
SociologySociology of Families: Comprehensive Revision
Dive into an extensive overview of family dynamics, perspectives, and patterns in sociology. This resource covers key concepts such as family diversity, gender roles, marriage, and the impact of social policies on family structures. Perfect for A-Level Sociology students preparing for Paper 2.
1273,2392,304
English LiteratureAn Inspector Calls: Character Insights
Explore in-depth analysis and key quotes for characters in J.B. Priestley's 'An Inspector Calls'. This resource covers Gerald Croft, Inspector Goole, Sheila Birling, Mrs. Birling, Eric Birling, and Eva Smith, focusing on themes of class, gender roles, and social responsibility. Ideal for students aiming for Grade 8 and above.
1025,231901
CriminologyWJEC Unit 4 Criminology
Criminology unit 4 detailed revision note
127,120124
CriminologyCriminology Theories Overview
Explore key criminology theories and their implications on crime and deviance. This comprehensive summary covers biological, psychological, and sociological perspectives, including labelling theory, right realism, and the impact of social campaigns on policy development. Ideal for A-Level criminology students seeking to understand the complexities of criminal behaviour and the factors influencing crime prevention strategies.
129,746211
English LiteratureRomeo and Juliet: Key themes
Key Romeo and Juliet themes and analysed quotes
106,619197
C
BiologyCell Biology and Cell structure
cell structures
92,6740
English LiteratureMacbeth: Guilt and Ambition
Explore the complex themes of guilt and ambition in Shakespeare's 'Macbeth'. This analysis covers key characters, including Macbeth and Lady Macbeth, their moral dilemmas, and the tragic consequences of their ambition. Ideal for students studying character motivations, thematic elements, and the psychological impact of power. Includes insights on the natural order, manipulation, and the descent into madness.
918,818392
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user