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.
Prime factors of 176=2×2––––––×2×2––––––×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, 176×11=22×22×11×11
=22×22×112=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.