Question

By what smallest number mist 180 be multiplied so that it becomes a perfect square ?Also ,find the square root of the number so obtained​

Answer 1

Answer:

The least number is 5 and the "square root" is 30.

Solution:

To find the "smallest number" by which 180 will be multiplied to get a "perfect square", we need to factorize 180 as under:

180 = 2 x 90

= 2 × 9 × 10

2 x 3 x 3 x 2 x 5

= 22 × 3² × 5 X X

Now, 5 is not in square. If 5 is in square, then derived number will be perfect square.

Hence, 180 must be multiplied by 5 to get a "perfect square" as shown below:

180 22 x 32 x 52 X 4 x 9 x 25 = 900

Now, the square of 900 = 30.