Question

by what smallest number must 180 be multiplied so that it becomes a perfect square also? find the square root of the number so obtained

Answer 1

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:

$180=2 \times 90$

$=2 \times 9 \times 10$

$=2 \times 3 \times 3 \times 2 \times 5$

$=2^{2} \times 3^{2} \times 5$

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:

$180=2^{2} \times 3^{2} \times 5^{2}=4 \times 9 \times 25=900$

Now, the square of 900 = 30

Answer 2

Answer:

here is your answer

Explanation:

hope it helped you