Fun National 5 Maths Surds Worksheets and Tips!

110

Hannah Murdoch

21/10/2025

Maths

Surds - National 5 Maths Revision

2,693

•

21 Oct 2025

•

2 pages

Fun National 5 Maths Surds Worksheets and Tips!

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Hannah Murdoch

@hannah_murdoch

National 5 Maths Surdsrevision guide provides essential information on... Show more

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.

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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Maths

21 Oct 2025

2,693

2 pages

Fun National 5 Maths Surds Worksheets and Tips!

Hannah Murdoch @hannah_murdoch

National 5 Maths Surdsrevision 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... Show more

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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!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Introduction to 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.