Find the smallest number by which 3645 must be divided so that it beco

1.	Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.
Answer» Given that, 3645 = (3 × 3) × (3 × 3) × 5 × 3 =3² × 3² × 5 × 3 To make the unpaired 5 and 3 into paired, the number 3645 has to be divided by 5 × 3=15 3645 ÷ 15 = 3² × 3² ∴ Square root , √(3645 ÷ 15) = 3 × 3 = 9

Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.

Answer»

Given that,

3645 = (3 × 3) × (3 × 3) × 5 × 3

=3² × 3² × 5 × 3

To make the unpaired 5 and 3 into paired, the number 3645 has to be divided by 5 × 3=15

3645 ÷ 15 = 3² × 3²

∴ Square root ,

√(3645 ÷ 15) = 3 × 3

= 9