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 becames a perfect square. Also, find the square root of the perfect square so obtained.
Answer» 180 = 2² × 3² × 5 = (2 × 2) × (3 × 3) × 5 To make the unpaired 5 into paired, multiply the number with 5 Therefore, 180 × 5 = 2² × 3² × 5² Hence, square root of number = \(\sqrt{180}\)x \(\sqrt{5}\) = 2 x 3 x 5 = 30

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

Answer»

180 = 2² × 3² × 5

= (2 × 2) × (3 × 3) × 5

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

180 × 5 = 2² × 3² × 5²

Hence, square root of number = \(\sqrt{180}\)x \(\sqrt{5}\) = 2 x 3 x 5

= 30