Checking and securing understanding of roots and integer indices | Maths

Starter quiz

What is the lowest common multiple of 12 and 14?

'84' ✓
What is the lowest common multiple of 12 and 15?

'60' ✓
What is the lowest common multiple of 12 and 16?

'48' ✓
What is the highest common factor of 12, 16 and 20?

'4' ✓
What is the highest common factor of 12 and 18?

'6' ✓
What is the highest common factor of 12 and 15?

'3' ✓

Exit quiz

Calculate $10^2 + 5^2$

'125' ✓
Calculate $9^2 + 3^3$

'108' ✓
Calculate $6^2 + 3^4$

'117' ✓
What is the value of A for: $10^2 + A^3 = 127$

'3' ✓
What is the value of A for: $A^2 + 6^3 = 360$

'12' ✓
Which is the best estimate for $\sqrt{32}$ (to 1 decimal place)?

6.1

5.3

5.7 ✓

Worksheet

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Lesson Details

Key learning points

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.

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).