Question

Find the smallest no. by which 240 must be multiplied to get a perfect sq.

Answer 1

240=2×2×2×2×5×3

For a number to be a perfect square, it must have its factors in pairs of two.

Here, 3 and 5 are not in pairs of two.

So we will have to multiply 240 by 3 and 5 i.e.

240×3×5=3600

√3600=60

Hence 240 has to be multiplied by 5 and 3 i.e. 15

Answer 2

we have to find out the smallest number which must be multiplied to 240 to make it a perfect square .

Let us  do prime factorization of 240 .

240 = 2 × 120 .

        = 2 × 2 × 60.

        = 2 × 2 × 2 × 30.

        = 2 × 2 × 2 × 2 × 3 × 5 .

Here we get 240 = 2⁴ × 3¹ × 5¹ .

∴ In order to make a perfect square 240 should be multiplied by 3 × 5 = 15

Ans :- The required number will be 15.