Question

So I am supposed to solve this without using a calculator: Sqrt[20]/10 - Sqrt[10]/Sqrt[32] - Sqrt[0.3125] + Sqrt[3 + 1/5]
You can put this into WolframAlpha as is to make it prettier.

Answer given is 1/2 * SQRT(5)

I really don't know where to start here. I have 5 sqrt rules in front of me along with 5 power rules.

Answer 1

Interpretation:

√20/10 - √10/√32 - √.3125 + √(3+1/5)

= 2√5/10 - √10/√32 * √32/√32 - √(5/16) + √(16/5)
= 2√5/10 - 8√5/32 - √5/4 + 4/√5 *√5/√5
= √5/5 - √5/4 - √5/4 + 4√5/5
= √5(1/5 - 1/4 - 1/4 + 4/5)
= (1/2)√5 or √5/2

Answer 2

Thank you Reiny, much appreciated!