Question

find the smallest number by which the given number must be multiplied so that the resulting number is a perfect square.
1. 23805
2. 12150
3. 7688

Answer 1

Solution:-

First of all,

First of all,We will take the L.C.M. of the Given Numbers and will multiply the given number to the unpaired Number.

(1) 23805.

L.C.M. of 23805 is

=) 23805 = 3 × 3 × 5 × 23 × 23.

In the Above list,

3 and 23 are in pair and only 5 is unpaired.

=) 23805 × 5

=) 119,025 is a Perfect Square.

(2) 12150.

L.C.M. of 12150 is

=) 12150 = 2 × 3 × 3 × 3 × 3 × 3 × 5 × 5.

In the Above list,

5 and 2 times 3 are in pair and ( 2 and 3) is unpaired.

=) 12150 × 6

12150 × 6=) 72,900

Hence, 72,900 is a Perfect Square.

(3) 7688.

L.C.M. of 7688 is

=) 7688 = 2 × 2 × 2 × 31 × 31.

In the Above list,

31 and 2 are in pair and only 2 is unpaired.

=) 7688 × 2

7688 × 2 =) 15,376.

Hence,

15, 376 is a Perfect Square.

Answer 2

HELLO MATES ❤

Refer to the attachment ⬆️