Foundation and Higher · powers and roots

Powers and roots.
A root undoes
a power.

and 2⁵ is not
2 times 5

a short way to write multiplying —

Power

5² means 5 × 5

small number: how many fives

step 1 of 4

Squares and roots

1. Squaring: multiply the number by itself.

2. Square root: what squared gives this?

✓ Know the squares up to 15² = 225

5² = 5 × 5 = 25

√25 = 5 undoes the square

√81 = 9 because 9 × 9 = 81

step 2 of 4

Cubes and cube roots

1. Cubing: use the number three times.

2. Cube root: what cubed gives this?

✓ Know the cubes of 1, 2, 3, 4, 5 and 10

2³ = 2 × 2 × 2 = 8

³√8 = 2 undoes the cube

³√125 = 5 5 × 5 × 5 = 125

step 3 of 4

Higher powers

1. The power counts how many 2s.

2. Double up: 2, 4, 8, 16, 32.

✓ On a calculator use the x^■ key

2⁵

= 2 × 2 × 2 × 2 × 2 five 2s

= 32 not 2 × 5 = 10

step 4 of 4

Estimate a root

1. Find the square numbers either side.

2. 50 is very close to 49, so just over 7.

✓ A good estimate: 7.1

√50 no exact answer

√49 = 7   √64 = 8

√50 is just over 7

≈ 7.1

powers and roots —

Power

how many times to multiply

Root

the number you started with

Estimate

use the squares either side

3² is 3 × 3 = 9.
It is never 3 × 2.

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