Question

Find the smallest number by which 9900 should be divided by so that the quotient is a perfect square.

Answer 1

Factorising 9900 , you will get :

2 × 2 × 3 × 3 × 5 × 5 × 11

Grouping the factors in pairs in such a way that the two factors are identical.

You will get 9900 = (2 ×2 )× ( 3 × 3) × ( 5 × 5 ) × 11

You can see that 11 is not forming a pair with a like factor so you must get rid of 7 .

Thus,you must divide 9900 by 11 so as to obtain a perfect square.

Hence, the smallest number by which 9900 must be divided so as to make it a perfect square is 7 and number so obtained is :

9900 ÷ 11 = (2×2)×(3×3)×(5×5)× 11 ÷ 11

900 = (2×2)×(3×3) × ( 5×5)

Square root of the number obtained is $\large{\mathrm{ \sqrt{900} }}$

= 2 × 3 × 5

= 30 .