New
New
Year 10
Foundation

Checking and securing understanding of roots and integer indices

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

New
New
Year 10
Foundation

Checking and securing understanding of roots and integer indices

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

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.

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.

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).

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.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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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