phepafalowl

2022-07-27

Rationalize the denominator and simplify.
$\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}$

suchonos6r

Expert

Solution:
$\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}×\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}\phantom{\rule{0ex}{0ex}}=\frac{\left(\sqrt{5}-\sqrt{2}{\right)}^{2}}{3}\phantom{\rule{0ex}{0ex}}=\frac{\left(\sqrt{5}{\right)}^{2}+\left(\sqrt{2}{\right)}^{2}-2\sqrt{10}}{3}\phantom{\rule{0ex}{0ex}}=\frac{7-2\sqrt{10}}{3}$

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