# Simplifying square root of an irrational

1. Jan 5, 2016

### erisedk

1. The problem statement, all variables and given/known data
Find [(3 - 51/2)/2]1/2

2. Relevant equations

3. The attempt at a solution
My calculator says (-1 + √5)/2
I have no idea how. Rationalising doesn't really do much good. Just tell me where to start.

2. Jan 5, 2016

### blue_leaf77

Multiplying the original expression with $\sqrt{2}/\sqrt{2}$ will give you $\sqrt{6-2\sqrt{5}}$ in the numerator. Then think of the terms under the radical as having the form of $(a-b)^2 = a^2-2ab+b^2$.

3. Jan 5, 2016

### erisedk

Could you please elaborate? I'm not getting anywhere. I assume you mean use something like completing the square but I can't do it.

4. Jan 5, 2016

### blue_leaf77

What do you get after multiplying the original expression with $\frac{\sqrt{2}}{\sqrt{2}}$?

5. Jan 5, 2016

### vela

Staff Emeritus
You could also try working the other direction. Find the square of $\frac{-1 + \sqrt 5}{2}$ and see how it simplifies.

6. Jan 5, 2016

### erisedk

Oh I got that, ie √(6-2√5) ÷ 2
I don't get what I'm supposed to do after this.

7. Jan 5, 2016

### blue_leaf77

It is √(6-2√5) ÷ 2. Then express the terms under the radical in the form I wrote in post #2, that is, write $6-2√5 = a^2+b^2-2ab$ . FInd the right pair of $a$ and $b$ such that the LHS is equal to RHS.

8. Jan 5, 2016

### erisedk

Got it! Thanks!