Math Experts: squareroot(3+2squareoot2) - squareroot( 3-....

[mcdaking8484]

cant figure this problem out for the life of me.

Use your calculator to find the value of the expression
square root(3+2squareoot2) - squareroot( 3-2squareroot2)

Show algebraically that the given expression is indeed the calculated value.

The calculated value is 2, i just need to show how i got it.THanks alot

 

[morson]

Let a = 3 + 2*sqrt(2), b = 3 - 2*sqrt(2)

Note, ab = 1, a + b = 6 (some helpful relationships)

Then the expression, which we'll call y, becomes:

y = sqrt(a) - sqrt(b)

Squaring:

y^2 = a - 2*sqrt(ab) + b

But ab = 1, and a + b = 6:

y^2 = 6 - 2
= 4

==> y = 2