Question

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

Answer 1

So for this, we will be simplifying √180 and √125 using the product rule of radicals (√ab = √a * √b)

Starting with √180: $\sqrt{180}=\sqrt{10} *\sqrt{18} =\sqrt{5} *\sqrt{2}*\sqrt{9} *\sqrt{2}=3*2*\sqrt{5} =6\sqrt{5}$

Now with √125: $\sqrt{125}=\sqrt{25}*\sqrt{5} =5\sqrt{5}$

Now that we have our simplified radicals, our equation looks like this: 6√5 - 5√5 + √5 . Combine everything, and your answer will be 2√5.