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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

Answer:

  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

Answer:

  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

Answer:

  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

Answer:

  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, __, __, __, __, __, __, __, __, __, __

Answer:

Power series

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

 
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