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Year 10 - Maths

Multiplication of 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 appreciate the structure that underpins multiplication of surds.

Key Notes

  • The square root operation is equivalent to the exponent 0.5 where the base is the term under the square root.
  • You can deduce this as squaring and square rooting are inverse operations.
  • Since the exponents for each term are the same, they can be combined.

Vocabulary To Learn

  • Surd: A surd is an irrational number expressed as the root of a rational number.
  • Radical: The root sign is the radical symbol.
  • Radicand: The radicand is the value inside the radical symbol.

Common Mistakes To Avoid

  • Pupils may not simplify after multiplying surds.

3 Quick Questions (With Answers)

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

The square root operation is equivalent to the exponent 0.5 where the base is the term under the square root. You can deduce this as squaring and square rooting are inverse operations.

2. Use this key word in a maths sentence and explain it clearly. 'Surd'

A surd is an irrational number expressed as the root of a rational number. 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 simplify after multiplying surds. Correction: Surds should always be written in their simplest form for the final answer.

More Lessons In This Unit

Browse all guides in the Year 10 Maths guide library.