# CLASS-8INTRODUCTION OF SQUARE & SQUARE ROOTS

SQUARE & SQUARE ROOTS

If a number is multiplied by itself, we get a ‘Squared Number’ , also called a ‘Perfect Square’. For example, 5 x 5 = 5², so 25 is a perfect square and 5 is said to be the square root of 25.

The symbol of the square root is √ or ( )½. Suppose the square root of x is y, if  x = y².

Therefore we write √25 = 5 or  ( 25 )½ =  5

There are some example of square root is given below –

8 x 8 = 8² = 64, so the square root of 64 is 8 ( √64 = 8 )

12 x 12 = 12² = 144, so the square root of 144 is 12 ( √144 = 12 )

If we multiply negative ( - ) value number by itself repeatedly then we will consider only the positive value of a square root.

5² = 25  or  (-5)² = 25  or   (± 5)² = 25,  so √25 = ± 5

Similarly, 11² = 121 or (-11)² = 121 or  (± 11)² = 121, so √121 = ± 11

13² = 169  or  (-13)² = 169  or  (± 13)² = 169, so √169 = ± 13

24² = 576  or  (-24)² = 576  or  (± 24)² = 576, so √576 = ± 24

To find the square root of a number –

There are two ways of finding the square roots of large numbers

1) by prime factorization,   2) by division