Question

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

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Answer 1

Answer:

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

hope helped!

Answer 2

The prime factorisation of 3645:

3645 = 3 x 3 x 3 x 3 x 3 x 3 x 5

Grouping the factors into pairs of equal factors, we get:

3645 = (3 x 3) x (3 x 3) x (3 x 3) x 5

The factor, 5 does not have a pair. Therefore, we must divide 3645 by 5 to make a perfect square. The new number is:

(3 x 3) x (3 x 3) x (3 x 3) = 729

Taking one factor from each pair on the LHS, the square root of the new number

is 3 x 3 x 3, which is equal to 27.