expression: \({4\over 3-2\sqrt{2}}\)

answer: \({12 +8 \sqrt{2}}\)

and please show step by step how you did it ^.^

Guest Oct 2, 2017

#1**+2 **

Simplify the following:

4/(3 - 2 sqrt(2))

Multiply numerator and denominator of 4/(3 - 2 sqrt(2)) by 2 sqrt(2) + 3:

(4 (2 sqrt(2) + 3))/((3 - 2 sqrt(2)) (2 sqrt(2) + 3))

(3 - 2 sqrt(2)) (2 sqrt(2) + 3) = 3×3 + 3×2 sqrt(2) - 2 sqrt(2)×3 - 2 sqrt(2)×2 sqrt(2) = 9 + 6 sqrt(2) - 6 sqrt(2) - 8 = 1:

(4 (2 sqrt(2) + 3))/(1)

(4 (2 sqrt(2) + 3))/(1) = 4 (2 sqrt(2) + 3):

4 (2 sqrt(2) + 3) =**8sqrt(2) + 12**

Guest Oct 2, 2017

#2**+2 **

\(\sqrt2\approx 1.414213562\)

I suppose you could just use closer and closer estimations of sqrt2 and see if the answers keep getting closer...

\( \sqrt2 \approx 1.4\\ {4\over 3-2\sqrt{2}}\approx {4\over 3-2*1.4}\approx \frac{4}{0.2}\approx 20\\ 12+8\sqrt2\approx 12+8*1.4=12+8+3.2=23.2\)

\(\sqrt2 \approx 1.41\\ {4\over 3-2\sqrt{2}}\approx {4\over 3-2*1.41}\approx \frac{4}{0.18}\approx 22.2\\ 12+8\sqrt2\approx 12+8*1.41=12+11.28=23.28\)

The answers are getting close, answer certainly passes reasonable checks :)

Melody
Oct 2, 2017