**Power and roots in maths**

The power of a number indicates the number of times the number is to be multiplied by itself. It is denoted by a small digit on right hand side top of the number.

For example: The number 2 raised to the power of 4 is written as 24.

In the above example, 2 is also referred to as the base number and 4 is the index, power or exponent.

A number raised to the power of 2 is called as square of the number.

A number raised to the power of 3 is called the cube of the number.

**Evaluating powers**

You can find the value of a number n raised to the power of m by multiplying n by itself m times.

For example:

24 = 2 x 2 x 2 x 2 = 16

**Practice Questions**

Q1. Solve the following

- 33
- 54
- 62

Answer:

- 33 = 3 x 3 x 3 = 81
- 54 = 5 x 5 x 5 x 5 = 625
- 62 = 6 x 6 = 36

- Any number raised to the power of 1 is the number itself.
- Any number raised to the power of 0 equals to 1.

**Rules for evaluating powers**

**Roots**

Roots is the opposite of power. You can find the root of any number by using division. The square root of a number n can be represented as √n.

**Practice Questions**

Q1. Find the square root of

- 64
- 25
- 144

Answer:

- 64 = 8 x 8, hence square root of 64 = 8
- 25 = 5 x 5, hence square root of 25 = 5
- 144 = 12 x 12, hence square root of 144 = 12

**Powers and root worksheet**

Q1: Solve the following:

- 23
- 53
- 104n
- 24 + 25
- 33 + 32
- 72

Answer:

- 23 = 2 x 2 x 2 = 8
- 53 = 5 x 5 x 5 = 125
- 104 = 10 x 10 x 10 x 10 = 10000
- 24 + 25 = 2(4 + 5) = 29 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512
- 33 + 32 = 3(3 + 2) = 35 = 243
- 72 = 7 x 7 = 49

Q2: Find the square root of

- 121
- 81
- 16

Answer:

- 121 = 11 x 11, hence square root of 121 = 11
- 81 = 9 x 9, hence square root of 81 = 9
- 16 = 4 x 4, hence square root of 16 = 4

Q3: Complete the following series:

1, 4, 9, 16, 25, __, __, __, __, __, __, __, __, __, __

Answer:

Power series

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

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