Question

What is the exact value of the expressions the square root of 180. − the square root 125. + the square root of 5.? Simplify if possible.
2 the square root of 2.
12 the square root of 2.
2 the square root of 5.
12 the square root of 5.

Answer 1

Rewrite √180 as √(6^2*5), pull terms out from under the radical to get 6√5

Rewrite √125 as √(5^2*5), pull terms out from under the radical to get 5√5

Now you have:

6√5 - 5√5 + √5 = 2√5 ( 2 the square root of 5.)