Question

Find the smallest number by which 3645 must be multiplied to get a perfect square.
find the square root of the resulting number.
Square roots and Cube Roots
Find the smallest number by which 7776 is to be divided to get a perfect square,
1521 trees are planted in a garden in such a way that there are as many trees in eac
13
2.
Find the smallest number by which 2400 is to be multiplied to get a perfect square and
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Answer 1

Given, a number as 3645. We need to find out a number which if multiplied by the given number we should get a perfect square.

Step 1: Resolve 3645 into prime factors

 5 3645

9 729

9 81

3 9

   3

We get, 5 × 9 × 9 × 3 × 3

Step 2: Pair the factors obtained

⇒ (9 × 9) × (3 × 3) × 5

Step 3: multiply the number with the factor which is alone.

Here, 9,3 are in pair and 5 is alone.

So,we must multiply the given number by 5 to get a perfect square.

⇒ 3645 × 5 = 18225.

Hence, 5 should be multiplied to the given number “3645” to make it perfect square.