Question

Question 98

Solve the following question:

Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.

Answer 1

Prime factors of $176=\underset{–}{2\times 2}\times \underset{–}{2\times 2}\times 11$
Here, 11 has no pair
So, it is not a perfect square and 11 is the smallest number by which 176 should be multiplied to get a perfect square.
Then, $176\times 11=2^2\times 2^2\times 11\times 11$
$=2^2\times 2^2\times {11}^2=1936=(44{)}^2$
which is a perfect square of 44
Hence, the smallest number is 11 by which it should be multiplied to get a perfect square.