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:
`√(180)=√(10) *√(18) =√(5) *√(2)*√(9) *√(2)=3*2*√(5) =6√(5)`

Now with √125:
`√(125)=√(25)*√(5) =5√(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.