Find the smallest number by which 180 must be multiplied so that it be

1.	Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.
Answer» Given, 180 = (2 × 2) × (3 × 3) × 5 =2² × 3² × 5 To make the unpaired 5 into paired, multiply the number with 5 180 × 5 = 2² × 3² × 5² ∴ Square root of √(180 × 5) = 2 × 3 × 5 = 30

Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.

Answer»

Given,

180 = (2 × 2) × (3 × 3) × 5

=2² × 3² × 5

To make the unpaired 5 into paired, multiply the number with 5

180 × 5 = 2² × 3² × 5²

∴ Square root of √(180 × 5) = 2 × 3 × 5

= 30