=SQRT((3*SQRT(80))+((3/(9+4*SQRT(5)))))

[Dartmski]

Can someone shed light on how to simply the following:

=SQRT((3*SQRT(80))+((3/(9+4*SQRT(5)))))

I started by squaring the whole equation to "get rid of" the overall sqrt, but then ran into problems when trying to simplying the fractions containing square roots. There seems to be the need to FOIL the denominator??

Thanks!

[Guest]

Is the answer 27?

[Jeff]

I believe the answer is 3sqrt(3). Kind of tough to show the steps in this format, but here's my attempt I'll use rt(x) to mean sqrt(x) to keep things a bit easier.

rt((3*rt(80)+(3/(9+4*rt(5)))))

Let's start by getting rid of the fraction by multiplying numerator and denominator by 9-4*rt(5)

rt((3*rt(80)+((27-12rt(5))))

Pretty neat that (9+4*rt(5))*(9-4*rt(5))=1!!

next see that 80=16*5 so

rt(3*4*rt(5)+27-12*rt(5))
the rt(5) terms cancel so we have
rt(27)
=3rt(3)

Jeff