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: