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

Simplify terms by rationalizing: Step 1: Simplify each term by rationalizing the denominators. For the first term, multiply numerator and denominator by sqrt6: (2sqrt5)/(sqrt6) * (sqrt6)/(sqrt6) = (2sqrt5 * sqrt6)/(6) = (2sqrt30)/6 = sqrt30/3 Simplify second term: Step 2: Simplify the second term similarly, multiply numerator and denominator by sqrt3: (2sqrt2)/(sqrt3) * (sqrt3)/(sqrt3) = (2sqrt2 * sqrt3)/(3) = (2sqrt6)/3 Add simplified terms: Step 3: Add the simplified terms from Step 1 and Step 2: sqrt30/3 + 2sqrt6/3 = (sqrt30 + 2sqrt6)/3

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Algebra 1

Multiply radical expressions

Full solution

Q. Evaluate:

\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 $2$ : $\newline$ $\frac{\sqrt{30}}{3} + \frac{2\sqrt{6}}{3}$ $\newline$ = $\frac{\sqrt{30} + 2\sqrt{6}}{3}$