Fun National 5 Maths Surds Worksheets and Tips!

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Hannah Murdoch

14/10/2022

Maths

Surds - National 5 Maths Revision

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Maths

Number

Surds

Fun National 5 Maths Surds Worksheets and Tips!

National 5 Maths Surds revision guide provides essential information on simplifying and working with surds. This comprehensive resource covers key concepts, rules, and examples to help students master surds for their National 5 Maths exams.

Defines surds and explains their properties
Covers simplification of surds and operations with surds
Provides step-by-step examples for simplifying complex surd expressions
Explains the process of rationalising denominators with surds
Includes practice problems to reinforce understanding

14/10/2022

A surd is
an
have
e.g. √2
and √25 = 5
have
Rules:
an
√a x √b = Jab
= 15 x 2
: 30
Nat S Maths Revision
Surds
square root (or cube root etc.)

Rationalising the Denominator

This page focuses on the important technique of rationalising the denominator when working with surds. This skill is crucial for National 5 Maths Surds past paper questions.

Definition: Rationalising the denominator means turning the surd at the bottom of a fraction into a whole number, while keeping the fraction the same.

The page explains that it's not possible to add or subtract surds with different surd signs. For example, √5 + √3 cannot be simplified further.

Highlight: Rationalising the denominator is important for various mathematical reasons and is a common requirement in National 5 Maths problems.

The method for rationalising the denominator is clearly explained: Multiply both the numerator and denominator by the surd in the denominator.

Three examples are provided to illustrate this process:

Rationalising 1/ $3√2$
Rationalising √8/√8
Rationalising 3√8/4

These examples demonstrate the step-by-step process of rationalising denominators with different types of surds, which is essential practice for National 5 Maths Surds revision worksheets.

Example: To rationalise 1/ $3√2$ , multiply both numerator and denominator by √2: $1 × √2$ / $3√2 × √2$ = √2 / 6

This page provides valuable practice for students preparing for National 5 Maths exams, where rationalising denominators is a common topic in Surds questions.

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Subjects

Maths

Number

Surds

Maths

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14 Oct 2022

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Fun National 5 Maths Surds Worksheets and Tips!

Hannah Murdoch

@hannah_murdoch

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Rationalising the Denominator

This page focuses on the important technique of rationalising the denominator when working with surds. This skill is crucial for National 5 Maths Surds past paper questions.

Definition: Rationalising the denominator means turning the surd at the bottom of a fraction into a whole number, while keeping the fraction the same.

The page explains that it's not possible to add or subtract surds with different surd signs. For example, √5 + √3 cannot be simplified further.

Highlight: Rationalising the denominator is important for various mathematical reasons and is a common requirement in National 5 Maths problems.

The method for rationalising the denominator is clearly explained: Multiply both the numerator and denominator by the surd in the denominator.

Three examples are provided to illustrate this process:

Rationalising 1/ $3√2$
Rationalising √8/√8
Rationalising 3√8/4

These examples demonstrate the step-by-step process of rationalising denominators with different types of surds, which is essential practice for National 5 Maths Surds revision worksheets.

Example: To rationalise 1/ $3√2$ , multiply both numerator and denominator by √2: $1 × √2$ / $3√2 × √2$ = √2 / 6

This page provides valuable practice for students preparing for National 5 Maths exams, where rationalising denominators is a common topic in Surds questions.

Sign up to see the contentIt's free!

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Introduction to Surds

This page introduces the concept of surds in National 5 Maths. Surds are square roots $or other roots$ that do not have an exact answer. The page covers basic definitions, properties, and rules for working with surds.

Definition: A surd is a square root $or cube root, etc.$ which does not have an exact answer.

Example: √2 = 1.414213... is a surd, while √25 = 5 is not a surd because it has an exact answer.

The page outlines important rules for working with surds:

√a × √b = √ $ab$
√ $x × x$ = x

Three detailed examples are provided to illustrate these concepts:

Simplifying the product of surds: 3√2 × 5√2
Expressing √48 and √98 in their simplest form
Simplifying a complex surd expression: √63 + √7 - √28

These examples demonstrate the step-by-step process of simplifying surds, which is crucial for National 5 Maths Surds revision.

Highlight: Understanding how to simplify surds is essential for solving more complex problems in National 5 Maths.

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Fun National 5 Maths Surds Worksheets and Tips!

Rationalising the Denominator

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Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

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21 M

#1

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Still not convinced? See what other students are saying...

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

The app is very simple and well designed. So far I have always found everything I was looking for :D

I love this app ❤️ I actually use it every time I study.

Fun National 5 Maths Surds Worksheets and Tips!

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Rationalising the Denominator

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Introduction to Surds

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