Solve frac{8sqrt{15}}{2sqrt{5}}

$$\frac { 8 \sqrt { 15 } } { 2 \sqrt { 5 } }$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{4\sqrt{15}}{\sqrt{5}}$$

Rationalize the denominator of \frac{4\sqrt{15}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{4\sqrt{15}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{4\sqrt{15}\sqrt{5}}{5}$$

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

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Cancel out 5 and 5.

$$4\sqrt{3}$$