How do you simplify $\frac{\sqrt{5}}{5 + \sqrt{2}}$ $sqrt5/(5+sqrt2)$ ?

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How do you simplify $\frac{\sqrt{5}}{5 + \sqrt{2}}$ $sqrt5/(5+sqrt2)$ ?

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Answer 1 · 2017-05-30T12:50:04

See below.

Explanation:

To simplify, we have to multiply by the conjugate of the denominator, or $5 - \sqrt{2}$ $5-sqrt2$ .

$\frac{\sqrt{5}}{5 + \sqrt{2}} \cdot \frac{5 - \sqrt{2}}{5 - \sqrt{2}} = \frac{5 \sqrt{5} - \sqrt{10}}{25 - 2} = \frac{5 \sqrt{5} - \sqrt{10}}{23}$ $sqrt5/(5+sqrt2)\cdot(5-sqrt2)/(5-sqrt2)=(5sqrt5-sqrt10)/(25-2)=(5sqrt5-sqrt10)/(23)$

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How do you simplify $\frac{\sqrt{5}}{5 + \sqrt{2}}$ $sqrt5/(5+sqrt2)$ ?

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