Surds are square roots that can't be simplified into whole...
Maths846 views·Updated 18 Aug 2026·2 pagesUnderstanding and Working with Surds
Leah Strawbridge@leahstrawbridge_kjnx
1
of 2
What Are Surds?
Ever wondered why some square roots just won't turn into neat numbers? That's exactly what surds are - square roots that refuse to become rational numbers (whole numbers or fractions).
Take √2 or √5 - these are perfect examples of surds because they can't be simplified further. However, √81 might look like a surd at first glance, but it actually equals 9, so it's not a real surd.
The key to simplifying surds is hunting for square number factors. For example, with √20, you'd spot that 4 is a factor of 20 and 4 is a perfect square. This means √20 = √(4 × 5) = √4 × √5 = 2√5.
Quick Tip: Always look for the largest square number that divides into your number - it'll save you time and effort!
2
of 2
Adding, Subtracting and Multiplying Surds
Adding and subtracting surds follows a simple rule: the surd parts must match! Think of it like collecting like terms in algebra. 4√3 + 5√3 = 9√3 because both terms have √3.
When the surds don't match initially, like √48 + √27, you'll need to simplify first. √48 becomes 4√3 and √27 becomes 3√3, giving you 4√3 + 3√3 = 7√3. Subtraction works exactly the same way: 6√5 - 2√5 = 4√5.
Multiplying surds is actually quite straightforward. You can multiply the numbers under the square root signs together: √2 × √98 = √196 = 14. When you have coefficients (numbers in front), multiply those separately: 3√2 × 5√3 = 15√6.
Remember: √a × √b = √(a × b) - this rule will be your best friend in surd calculations!
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Maths846 views·Updated 18 Aug 2026·2 pagesUnderstanding and Working with Surds
Leah Strawbridge@leahstrawbridge_kjnx
Surds are square roots that can't be simplified into whole numbers or fractions - they're really useful in maths when you need exact answers rather than decimals. Don't worry, they're not as scary as they look, and once you get...
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of 2
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What Are Surds?
Ever wondered why some square roots just won't turn into neat numbers? That's exactly what surds are - square roots that refuse to become rational numbers (whole numbers or fractions).
Take √2 or √5 - these are perfect examples of surds because they can't be simplified further. However, √81 might look like a surd at first glance, but it actually equals 9, so it's not a real surd.
The key to simplifying surds is hunting for square number factors. For example, with √20, you'd spot that 4 is a factor of 20 and 4 is a perfect square. This means √20 = √(4 × 5) = √4 × √5 = 2√5.
Quick Tip: Always look for the largest square number that divides into your number - it'll save you time and effort!
2
of 2Sign up to see the content. It's free!
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By signing up you accept Terms of Service and Privacy Policy
Adding, Subtracting and Multiplying Surds
Adding and subtracting surds follows a simple rule: the surd parts must match! Think of it like collecting like terms in algebra. 4√3 + 5√3 = 9√3 because both terms have √3.
When the surds don't match initially, like √48 + √27, you'll need to simplify first. √48 becomes 4√3 and √27 becomes 3√3, giving you 4√3 + 3√3 = 7√3. Subtraction works exactly the same way: 6√5 - 2√5 = 4√5.
Multiplying surds is actually quite straightforward. You can multiply the numbers under the square root signs together: √2 × √98 = √196 = 14. When you have coefficients (numbers in front), multiply those separately: 3√2 × 5√3 = 15√6.
Remember: √a × √b = √(a × b) - this rule will be your best friend in surd calculations!
We thought you’d never ask...
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.
You can download the app from Google Play Store and Apple App Store.
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