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Year 10 - Maths

Simplifying surds

Surds

Unit Summary

In this unit pupils will learn how to recognise surds, handle them in calculations and rationalise fractions with surds as denominators.

Lesson Summary

You will learn to simplify surds.

Key Notes

  • The radicand should be as small as possible.
  • If any of the radicand's factors are square numbers then the surd can be simplified.
  • Algebraic factors that are square values also mean the surd can be simplified.

Vocabulary To Learn

  • Product of primes: Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.
  • Simplest form: A surd is in its simplest form when the radicand is an integer with no perfect square factors greater than 1.

Common Mistakes To Avoid

  • Pupils may not multiply the existing coefficient with the coefficient of the simplified surd.

3 Quick Questions (With Answers)

1. Solve this in steps: explain the method from this lesson and why each step matters.

The radicand should be as small as possible. If any of the radicand's factors are square numbers then the surd can be simplified.

2. Use this key word in a maths sentence and explain it clearly. 'Product of primes'

Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers. Use this word when showing your method, then check your final answer is reasonable.

3. Spot and fix this common maths mistake.

Mistake: Pupils may not multiply the existing coefficient with the coefficient of the simplified surd. Correction: Replace the unsimplified surd with the simplified form within the original expression so pupils can see they need to multiply coefficients.

More Lessons In This Unit

Browse all guides in the Year 10 Maths guide library.