Question

Find the smallest number by which 3645 must be divided so that the
quotient is a perfect square. Also find the square root of the square
number so obtained.​

Answer 1

Answer:

$\bigstar$ The smallest number by which 3645 must be divided so that the quotient is a perfect square is 5.              

$\bigstar$ The square root of the square number so obtained = 27

Step-by-step explanation:

For finding the smallest number by which 3645 must be divided so that the quotient is a perfect square.

First we have to prime factorize 3645,

3645 = 3×3×3×3×3×3×5

On grouping the factors into pairs , we get

3645 = (3×3)×(3×3)×(3×3)×5

The only factor without a pair is 5 .

∴ The smallest number by which 3645 must be divided so that the

quotient is a perfect square is '5' .

Now to Find the Square Number we must divide 3645 by 5

3645 / 5 = 729

Next we have to find the Square root of 729

$\sqrt{729} = 27$

The square root of 729 = 27.