How do you simplify the square root of 176?

Look for factors that are perfect squares:

1, 4, 9, 16, 25, etc.

In this case, 16 is a factor (16 x 11 = 176):

so sqrt(176) = sqrt(16)*sqrt(11)

since 4*4 = 16, then sqrt(16)=4, you can simplify to:

4*sqrt(11)