## Solve, by steps: (1/sqrt[5]+1/sqrt[2]):(sqrt[5]+sqrt[2])

Simple patterns, variables, the order of operations, simplification, evaluation, linear equations and graphs, etc.
MathDrudge
Posts: 11
Joined: Sun Jul 24, 2011 10:17 am
Contact:

### Solve, by steps: (1/sqrt[5]+1/sqrt[2]):(sqrt[5]+sqrt[2])

$(\frac{1}{sqrt5}\, +\, \frac{1}{sqrt2}\,) :\, (\sqrt{5}\, +\, \sqrt{2})$

MathDrudge
Posts: 11
Joined: Sun Jul 24, 2011 10:17 am
Contact:

### Re: Solve, by steps

$(\frac{1}{sqrt5}\, +\, \frac{1}{sqrt2}\,) :\, (\sqrt{5}\, +\, \sqrt{2})$

$(\frac{sqrt{2}\, +\, sqrt{5}}{sqrt10}\,) :\, (\sqrt{5}\, +\, \sqrt{2})$

$(\frac{sqrt{2}\, +\, sqrt{5}}{sqrt10}\,) :\, (\frac{\sqrt{5}\, +\, \sqrt{2}}{1})$

$\frac{sqrt{2}\, +\, sqrt{5}}{sqrt10}\, *\, \frac{1}{\sqrt{5}\, +\, \sqrt{2}} =\, \frac{sqrt{2}\, +\, sqrt{5}}{sqrt10\, \sqrt{5}\, +\, \sqrt{2}}\, =\, \frac{1}{sqrt10}$ ?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
MathDrudge wrote:$(\frac{1}{sqrt5}\, +\, \frac{1}{sqrt2}\,) :\, (\sqrt{5}\, +\, \sqrt{2})$

Is the colon (the ":" symbols between the two sets of parentheses) meant to indicate division, or some other operation? Also, were the instructions really to "solve" (in which case, the rest of the equation is needed) or perhaps actually to "simplify"?

Thank you!

MathDrudge
Posts: 11
Joined: Sun Jul 24, 2011 10:17 am
Contact:

### Re: Solve, by steps: (1/sqrt[5]+1/sqrt[2]):(sqrt[5]+sqrt[2])

That is all of the problem, I meant simplify in that case. yes it is division

maggiemagnet
Posts: 351
Joined: Mon Dec 08, 2008 12:32 am
Contact:

### Re: Solve, by steps

MathDrudge wrote:$\frac{sqrt{2}\, +\, sqrt{5}}{sqrt10}\, *\, \frac{1}{\sqrt{5}\, +\, \sqrt{2}} =\, \frac{sqrt{2}\, +\, sqrt{5}}{sqrt10\, \sqrt{5}\, +\, \sqrt{2}}\, =\, \frac{1}{sqrt10}$ ?

The denominator should involve some grouping, shouldn't it?

$\frac{sqrt{2}\, +\, sqrt{5}}{sqrt{10}}\, \times\, \frac{1}{\sqrt{5}\, +\, \sqrt{2}}\, =\, \frac{sqrt{2}\, +\, sqrt{5}}{sqrt{10}\,\left( \sqrt{5}\, +\, \sqrt{2}\right)}$

Then the steps make sense. And you can check your work by plugging this into a calculator. If the decimal approximations are exactly the same for the first expression and your answer, then you simplified to the right thing.