How do you rationalize the denominator and simplify $\sqrt{\frac{5}{10}}$ $sqrt(5/10)$ ?

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How do you rationalize the denominator and simplify $\sqrt{\frac{5}{10}}$ $sqrt(5/10)$ ?

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Answer 1 · 2016-04-18T05:16:06

$\frac{\sqrt{2}}{2}$ $sqrt2/2$

Explanation:

First, we can simplify what's in the big root sign:
$\sqrt{\frac{5}{10}} = \sqrt{\frac{1}{2}}$ $sqrt(5/10)=sqrt(1/2)$
And we can split the big root sign into two smaller ones:
$= \frac{\sqrt{1}}{\sqrt{2}}$ $=sqrt1/sqrt2$
$= \frac{1}{\sqrt{2}}$ $=1/sqrt2$
Now we do something unexpected, and put another term into the equation.
$= \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$ $=1/sqrt2*sqrt2/sqrt2$
We can do this because $\frac{\sqrt{2}}{\sqrt{2}}$ $sqrt2/sqrt2$ is just 1, and anything times 1 is itself. Moreover we do this because the question asks us to rationalise the denominator, asking to remove any root signs.
$= \frac{\sqrt{2}}{\sqrt{2} \cdot \sqrt{2}}$ $=sqrt2/(sqrt2*sqrt2)$
$= \frac{\sqrt{2}}{2}$ $=sqrt2/2$

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How do you rationalize the denominator and simplify $\sqrt{\frac{5}{10}}$ $sqrt(5/10)$ ?

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How do you rationalize the denominator and simplify sqrt(5/10)√510sqrt(5/10)?

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How do you rationalize the denominator and simplify $\sqrt{\frac{5}{10}}$ $sqrt(5/10)$ ?