# How do you simplify #sqrt(3-2*sqrt(2))#?

##### 2 Answers

We have that

Take the needed answer form with variables and solve for them

#### Explanation:

The answer above is completely correct, but it may help the student to see how to reach it:

We seek a square root of

So

and

These are two simultaneous equations for

Rearrange the second:

Substitute into the first:

Note that this is a quadratic in

Factorise:

This gives us two possible solutions for

We are looking for integer solutions for

Now use the second equation to deduce the four equivalent solutions for

So we have the four solution pairs

This is a bit suspicious - we expect only two solutions, positive and negative square roots, so we wonder if some of these are identical to each other: When we substitute them in to our desired expression

So the two solutions with

When we take the written square root of a quantity, it is implied that the desired root is the positive root, the "principal value" of the square root function. So we take the single solution that comes from

Double check: Make sure that this produces the desired answer: