Question

14. 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 1

Step-by-step explanation:

Given number is 3645

write down the prime factors of 3645

3645= 5×3×3×3×3×3×3

prime factors into pairs

3645=(3×3)(3×3)(3×)×5

5 doesn't exists in pair

so the smallest number be divided from 3645 to make it perfect square is 5

3645÷5= 729

√729=27

27 is the sqaure root of resulting number 729.

Hope it helped..

Answer 2

Answer: first you have to do prime factorization for 3645 .

Then you will get  5 x 3 x 3 x 3 x 3 x 3 x 3

Then you have to pair them into squares

= 5 x 3 square x 3 square x 3 square  

so, the no.5 was not paired with any number.

so, you have to divide 3465 with 5

then you will get 693.

now, 693= 3 square x 3 square x 3 square

square root of 729 = the square root of 3 square x 3 square x 3 square.

you have to cancel the squares and the square roots.

so, square root of 729=3 x 3 x 3

square root of 729= 27

Hence the smallest number to be divided by 3645  to make it a perfect square = 729 and the square root of it =27.

HOPE I HELPED