Question

Find the smallest number by which 1008 must be multiplied to get a perfect square. also, find the square root of the perfect square so obtained

Answer 1

1. 7

2. square root is 84.

Explanation:

First find the prime factors:

1008 =2*2*2*2*3*3*7

There's an even number of 2's and 3's but only one 7, so we multiply by 7

Smallest number = 7.

The square number is 1008 * 7

= 7056.

Its square root is 2*2*3*7 = 84.

Answer 2

7

Explanation:

we have 1008=2×2××2×3×3×3

The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.

Now 1008×7=2×2×2×2×3×3×7×7

7056=2×2×3×7

=84

Answer : 7