# Simplify this simple expression?

So the expression is $-(1/3)(1/2)^{3/2} + 1/3 - (1/3)(1/\sqrt{2})^3$.

The answer in my book is $1/3(1 - 1/\sqrt{2})$. But that simplifies to $1/3 - 1/3\sqrt{2}$. How come it isn't $1/3 + 2(-1/\sqrt{2})$, which is what I got.

• This tutorial explains how to typeset mathematics on this site. – N. F. Taussig Apr 25 '18 at 1:21
• Because... you did it wrong? How can we answer why you got the wrong answer if we don't know how you got the wrong answer. – fleablood Apr 25 '18 at 1:27
• Probably because you didnt add of the two terms that are essential $(\frac 12)^{\frac 32}$ properly. $(\frac 12)^{\frac 32} = \frac 1{2\sqrt 2}$ and so $2*\frac 1{2\sqrt 2} = \frac 1{\sqrt 2}$. – fleablood Apr 25 '18 at 1:40
• Sorry I'm asking on a smartphone but got your answer thx! – Edon Knoul Apr 25 '18 at 1:57

$−\frac 13(\frac 12)^{\frac 32}+\frac 13 −\frac 13(\frac 1{\sqrt 2})^3=$

$\frac 13[-(\frac 12)^{\frac 32}+1 - (\frac 1{\sqrt 2})^3]=$

$\frac 13[-(\frac 12)^{\frac 32}+1 - (\frac 1{2})^{\frac 32}]=$

$\frac 13[1 - 2*(\frac 1{2})^{\frac 32}]=$

$\frac 13[1 - 2*(\frac 1{2})^{1+\frac 12}]=$

$\frac 13[1 - 2*(\frac 1{2})^{1}(\frac 12)^{\frac 12}]=$

$\frac 13[1- \frac 12^{\frac 12}]=$

$\frac 13 - \frac 1{3\sqrt 2}$

• @N.F.Taussig I suppose fleablood should be familiar with those, given the amount of reputation he has. – user330477 Apr 25 '18 at 1:44
• Well, good for you. I guess... – fleablood Apr 25 '18 at 4:46
• I deleted my answer since your answer is more complete. – N. F. Taussig Apr 25 '18 at 10:22