Question

Find the smallest number by which 3645 must divided so that it become a perfect square?also find the square root of the resulting number.​

Answer 1

Given number is 3645

Jot 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 doesnt 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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Answer 2

the prime factors of 3645 =5×3×3×3×3×3×3

organising the prime factors in to pairs

(3×3) (3×3)(3×3)×5

we observe that the only 5 is not exists integers

so the smallest number that should divide by the number 3645 is 5

3645÷5

=729

the square root of 729 is 27