Evaluate square root of 5/6

Problem

$\sqrt{\frac{5}{6}}$

Solution

1. Apply the quotient rule for radicals to separate the square root of the numerator and the denominator.

$\sqrt{\frac{5}{6}}=\frac{\sqrt{5}}{\sqrt{6}}$

2. Rationalize the denominator by multiplying both the numerator and the denominator by $\sqrt{6}$

$\frac{\sqrt{5}}{\sqrt{6}}\cdot \frac{\sqrt{6}}{\sqrt{6}}$

3. Multiply the radicals in the numerator and simplify the denominator.

$\frac{\sqrt{5\cdot 6}}{6}$

4. Simplify the expression by performing the multiplication inside the radical.

$\frac{\sqrt{30}}{6}$

Final Answer

$\sqrt{\frac{5}{6}}=\frac{\sqrt{30}}{6}$

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