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Year 10 - Maths

Checking and securing understanding of roots and integer indices

Arithmetic procedures: index laws

Unit Summary

In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.

Lesson Summary

You will learn to calculate with roots and integer indices, including estimating the answer.

Key Notes

  • Integer indices state how often a number should be multiplied by itself.
  • The square root of any perfect square will be an integer.
  • The square root of any number can be found using a calculator but it may not be an integer.
  • The square root of any number can be estimated by comparing the square roots of the closest perfect squares.

Vocabulary To Learn

  • Indices: An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication. An alternative word for this is index (plural indices).

Common Mistakes To Avoid

  • Any number is a square or cube number because it can be squared or cubed.

3 Quick Questions (With Answers)

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

Integer indices state how often a number should be multiplied by itself. The square root of any perfect square will be an integer.

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

An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication. An alternative word for this is index (plural indices). Use this word when showing your method, then check your final answer is reasonable.

3. Spot and fix this common maths mistake.

Mistake: Any number is a square or cube number because it can be squared or cubed. Correction: A square number is the result of a number being multiplied by itself. Emphasis must be on the result. A cube number is a number that has been multiplied by itself three times. Emphasis must be on the result of the repeated multiplication.

More Lessons In This Unit

Browse all guides in the Year 10 Maths guide library.