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(2sqrt5)/(sqrt6)+(2sqrt2)/(sqrt3)

$\frac{2\sqrt{5}}{\sqrt{6}} + \frac{2\sqrt{2}}{\sqrt{3}}$

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Multiply radical expressions

Full solution

Q.

\frac{2\sqrt{5}}{\sqrt{6}} + \frac{2\sqrt{2}}{\sqrt{3}}

Simplify terms by rationalizing: Step $1$ : Simplify each term by rationalizing the denominators. $\newline$ For the first term, multiply numerator and denominator by $\sqrt{6}$ : $\newline$ $\frac{2\sqrt{5}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{2\sqrt{5} \times \sqrt{6}}{6}$ $\newline$ = $\frac{2\sqrt{30}}{6}$ $\newline$ = $\frac{\sqrt{30}}{3}$
Simplify second term: Step $2$ : Simplify the second term similarly, multiply numerator and denominator by $\sqrt{3}$ : $\frac{2\sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{2\sqrt{2} \times \sqrt{3}}{3}$ = $\frac{2\sqrt{6}}{3}$
Add simplified terms: Step $3$ : Add the simplified terms from Step $1$ and Step $2$ : $\newline$ $\frac{\sqrt{30}}{3} + \frac{2\sqrt{6}}{3}$ $\newline$ = $\frac{\sqrt{30} + 2\sqrt{6}}{3}$

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