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

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

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

MathDrudge
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### 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
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$(\frac{1}{sqrt5}\, +\, \frac{1}{sqrt2}\,) :\, (\sqrt{5}\, +\, \sqrt{2})$
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
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### 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
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### Re: Solve, by steps

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

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