Solve frac{sqrt{60^circ}}{8sqrt{3}}

$$\frac { \sqrt { 60 ^ { \circ } } } { 8 \sqrt { 3 } }$$

Evaluate

$$\frac{\sqrt{5}}{4}\approx 0.559016994$$

Solution Steps

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$\frac{2\sqrt{15}}{8\sqrt{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{15}}{4\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{15}}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{15}\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{15}\sqrt{3}}{4\times 3}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$\frac{\sqrt{3}\sqrt{5}\sqrt{3}}{4\times 3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3\sqrt{5}}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{3\sqrt{5}}{12}$$

Divide 3\sqrt{5} by 12 to get \frac{1}{4}\sqrt{5}.

$$\frac{1}{4}\sqrt{5}$$