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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

1. 33
2. 54
3. 62

1. 33 = 3 x 3 x 3 = 81
2. 54 = 5 x 5 x 5 x 5 = 625
3. 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

1. 64
2. 25
3. 144

1. 64 = 8 x 8, hence square root of 64 = 8
2. 25 = 5 x 5, hence square root of 25 = 5
3. 144 = 12 x 12, hence square root of 144 = 12

Powers and root worksheet

Q1: Solve the following:

1. 23
2. 53
3. 104n
4. 24 + 25
5. 33 + 32
6. 72

1. 23 = 2 x 2 x 2 = 8
2. 53 = 5 x 5 x 5 = 125
3. 104 = 10 x 10 x 10 x 10 = 10000
4. 24 + 25 = 2(4 + 5) = 29 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512
5. 33 + 32 = 3(3 + 2) = 35 = 243
6. 72 = 7 x 7 = 49

Q2: Find the square root of

1. 121
2. 81
3. 16

1. 121 = 11 x 11, hence square root of 121 = 11
2. 81 = 9 x 9, hence square root of 81 = 9
3. 16 = 4 x 4, hence square root of 16 = 4

Q3: Complete the following series:

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