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New
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Year 10
Higher

Checking and securing understanding of roots and integer indices

I can calculate with roots and integer indices, including estimating the answer.

icon-background-square
New
New
Year 10
Higher

Checking and securing understanding of roots and integer indices

I can calculate with roots and integer indices, including estimating the answer.

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Lesson details

Key learning points

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

Keywords

  • 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 misconception

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

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.


To help you plan your year 10 maths lesson on: Checking and securing understanding of roots and integer indices, download all teaching resources for free and adapt to suit your pupils' needs...

When estimating the answer to a root of a number, pupils must know which square roots of a perfect square are either side of this number to make an estimate. For example, sqrt 15 is in-between sqrt 9 and sqrt 16. This can be a quick fire round.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
What is the lowest common multiple of 12 and 14?
Correct Answer: 84
Q2.
What is the lowest common multiple of 12 and 15?
Correct Answer: 60
Q3.
What is the lowest common multiple of 12 and 16?
Correct Answer: 48
Q4.
What is the highest common factor of 12, 16 and 20?
Correct Answer: 4
Q5.
What is the highest common factor of 12 and 18?
Correct Answer: 6
Q6.
What is the highest common factor of 12 and 15?
Correct Answer: 3

6 Questions

Q1.
Calculate $$10^2 + 5^2$$
Correct Answer: 125
Q2.
Calculate $$9^2 + 3^3$$
Correct Answer: 108
Q3.
Calculate $$6^2 + 3^4$$
Correct Answer: 117
Q4.
What is the value of A for: $$10^2 + A^3 = 127$$
Correct Answer: 3, A = 3
Q5.
What is the value of A for: $$A^2 + 6^3 = 360$$
Correct Answer: 12, A=12
Q6.
Which is the best estimate for $$\sqrt{32}$$ (to 1 decimal place)?
6.1
5.3
Correct answer: 5.7