# Rationalize the denominator. displaystylefrac{sqrt{{40}}}{sqrt{{56}}}

Rationalize the denominator.
$\frac{\sqrt{40}}{\sqrt{56}}$
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Step 1
We write them under one radical. Then recue $\frac{40}{56}$ by 8.
$=\frac{\sqrt{40}}{\sqrt{56}}$
$=\sqrt{\frac{40}{56}}$
$=\sqrt{\frac{40÷8}{56÷8}}$
$=\sqrt{\frac{5}{7}}$
Step 2
Separate the radicals. And multiply numerator and denominator by $\sqrt{7}$
$\sqrt{\frac{5}{7}}$
$=\frac{\sqrt{5}}{\sqrt{7}}$
$=\frac{\sqrt{5}×\sqrt{7}}{\sqrt{7}×\sqrt{7}}$
$==\frac{\sqrt{35}}{7}$
Answer: $\frac{\sqrt{35}}{7}$