To square a number we multiply the number by itself.

3 squared is 9 because 3 × 3 = 9

4 squared is 16 because 4 × 4 = 16

We can write squared using a small (superscript) 2.

5² means 5 squared

10² means 10 squared

**
Example 1: Work out the value of 9²
**

To work out the value of 9 squared we need to calculate 9 × 9

9 × 9 = 81

9² = 81

**
Example 2: Work out the value of (-8)²
**

To work out the value of -8 squared we need to calculate -8 × -8

-8 × -8 = 64 (A negative times a negative is a positive)

(-8)² = 64

If you are using a calculator you must put the -8 in brackets, otherwise the calculator will get the answer wrong!

**Try these:**

To cube a number we multiply the number by itself, and then multiply that answer by the number again.

We can write cubed using a small (superscript) 3.

2³ means 2 cubed

3³ means 3 cubed

**
Example 3: Work out the value of 4³
**

To work out the value of 4 cubed we need to calculate 4 × 4 × 4

4 × 4 = 16

16 × 4 = 64

4³ = 64

**
Example 4: Work out the value of 10³
**

To work out the value of 10 cubed we need to calculate 10 × 10 × 10

10 × 10 = 100

100 × 10 = 1000

10³ = 1000

**Try these:**

Square rooting is the opposite of sqauring a number.

9² = 81, so the square root of 81 is 9

Square root 100 can be written as √100

√81 means square root 81

**
Example 5: Work out the value of √144
**

We are looking for the number that multiplies by itself to make 144

12 × 12 = 144

√144 = 12

**
Example 6: Work out the value of √100
**

We are looking for the number that multiplies by itself to make 100

10 × 10 = 100

√100 = 10

**Try these:**

Cube rooting is the opposite of cubing a number.

10³ = 1000, so the square root of 1000 is 10

Cube root 125 can be written as ∛125

∛216 means cube root 216

**
Example 7: Work out the value of ∛8
**

We are looking for the number that multiplies by itself, and then by itself again, to make 8

2 × 2 × 2 = 8

∛8 = 2

**Try this:**

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