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Year 10 - Maths

Addition with 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 addition of surds.

Key Notes

  • An unknown value is represented by a letter.
  • An unevaluated surd can be thought of as an unknown value.
  • Each simplified surd has a unique value.
  • Surds can therefore be grouped in the same way as like terms.

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 think like surds need both the radicand and the coefficient to be the same.

3 Quick Questions (With Answers)

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

An unknown value is represented by a letter. An unevaluated surd can be thought of as an unknown value.

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 think like surds need both the radicand and the coefficient to be the same. Correction: Remind them of the distributive law: a(b+c) = ab + ac.

More Lessons In This Unit

Browse all guides in the Year 10 Maths guide library.