Find the smallest number by which 1152 must be divided so that it beco

1.	Find the smallest number by which 1152 must be divided so that it becomes a square. Also, find the square root of the number so obtained.
Answer» As understood we calculate prime factor of, 1152 = (2 × 2) × (2 × 2) × (2 × 2) × 2 × (3 × 3) =2² × 2² × 2² × 3² × 2 To make the unpaired 2 into paired, the number 1152 has to be divided by 2 1152 ÷ 2 = 2² × 2² × 2² × 3² ∴ Square root of √(1152 ÷ 2) = 2 × 2 × 2 × 3 = 24

Find the smallest number by which 1152 must be divided so that it becomes a square. Also, find the square root of the number so obtained.

Answer»

As understood we calculate prime factor of,

1152 = (2 × 2) × (2 × 2) × (2 × 2) × 2 × (3 × 3)

=2² × 2² × 2² × 3² × 2

To make the unpaired 2 into paired, the number 1152 has to be divided by 2

1152 ÷ 2 = 2² × 2² × 2² × 3²

∴ Square root of √(1152 ÷ 2) = 2 × 2 × 2 × 3

= 24