Question

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

Answer 1

iven number is 3645
Write down the prime factors of 3645
3645=5*3*3*3*3*3*3

Organising the prime factors into pairs

3645=(3*3)(3*3)(3*3)*5

We observe that only 5 doesn't exist in pair

So,the smallest number that should be divided from 3645 to make it a perfect square is 5

3645÷5= 729

Thus the resulting number is 729

√729=27

There fore , 27 is the square root of resulting number 729

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