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Year 10 - Maths

Applying the underlying structure of multiplication and division 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 multiply and divide with surds.

Key Notes

  • The multiplication of surds can be generalised.
  • √a × √b=√ab and √a × √(1/b) = √(a/b) = √a ÷ √b
  • You may be able to simplify this product.

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 insist that a square root can be both positive and negative.

3 Quick Questions (With Answers)

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

The multiplication of surds can be generalised. √a × √b=√ab and √a × √(1/b) = √(a/b) = √a ÷ √b.

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 insist that a square root can be both positive and negative. Correction: By convention, square root refers to the principal (positive) square root.

More Lessons In This Unit

Browse all guides in the Year 10 Maths guide library.