1.4 Powers and roots

Question 1

What is a square number?

Answer 1

A square number is a number that is multiplied by itself. For example, 5 squared (5 × 5) = 25.

Question 2

What is the square root of 25?

Answer 2

The square root of 25 is 5, because 5 × 5 = 25.

Question 3

What is a cube number?

Answer 3

A cube number is a number that is multiplied by itself twice. For example, 2 cubed (2 × 2 × 2) = 8.

Question 4

What is the cube root of 8?

Answer 4

The cube root of 8 is 2, because 2 × 2 × 2 = 8.

Question 5

How do you find the square of a number?

Answer 5

Multiply the number by itself. For example, the square of 4 is 4 × 4 = 16.

Question 6

How do you find the cube of a number?

Answer 6

Multiply the number by itself twice. For example, the cube of 3 is 3 × 3 × 3 = 27.

Question 7

What is the square root of 36?

Answer 7

The square root of 36 is 6, because 6 × 6 = 36.

Question 8

What is the cube root of 27?

Answer 8

The cube root of 27 is 3, because 3 × 3 × 3 = 27.

Question 9

Calculate 3²

Answer 9

3² = 3 × 3 = 9

Question 10

Calculate 72²

Answer 10

72² = 72 × 72 = 5184

Question 11

Calculate 112²

Answer 11

112² = 112 × 112 = 12544

Question 12

Calculate 212²

Answer 12

212² = 212 × 212 = 44944

Question 13

Calculate 192²

Answer 13

192² = 192 × 192 = 36864

Question 14

Calculate 322²

Answer 14

322² = 322 × 322 = 103684

Question 15

Calculate 1³

Answer 15

1³ = 1 × 1 × 1 = 1

Question 16

Calculate 33³

Answer 16

33³ = 33 × 33 × 33 = 35937

Question 17

Find x such that x × x = 25

Answer 17

x = 5

Question 18

Find x such that x × x × x = 8

Answer 18

x = 2

Question 19

Find x for x × x = 121.

Answer 19

x = 11

Question 20

Find x for x × x × x = 8000.

Answer 20

x = 20

Question 21

Find x for x × x = 225.

Answer 21

x = 15

Question 22

Find x for x³ = 2.

Answer 22

x = ∛2 (cube root of 2)

Question 23

Find x for x³ = 1.

Answer 23

x = 1

Question 24

Find x for 64³ = x.

Answer 24

x = 4