Question

1) Find the smallest number by which the number 216 should be
multiplied so as to get a perfect square number. Also find the
square root of the square number so obtained.​

Answer 1

Factors of 216 = 2 × 2 × 2 × 3 × 3 × 3

Now, grouping the prime factors = (2 × 2) × 2 × (3 × 3) × 3

Factors 2 and 3 has no pair.

∴ 216 is not a perfect square.

The smallest number it should be divided to get a perfect square is 3 × 2 = 6.

Then, = 216 ÷ 6 = 36

Factors of 36 = 6 × 6

√36 = √(6× 6)

= √(6)

= 6

∴ 36 is a perfect square and 6 is the square root of 36.