Solve (2)frac{4sqrt{15}}{sqrt{5}}

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

Evaluate

$$8\sqrt{3}\approx 13.856406461$$

Solution Steps

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

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

The square of \sqrt{5} is 5.

$$2\times \frac{4\sqrt{15}\sqrt{5}}{5}$$

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}.

$$2\times \frac{4\sqrt{5}\sqrt{3}\sqrt{5}}{5}$$

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

$$2\times \frac{4\times 5\sqrt{3}}{5}$$

Cancel out 5 and 5.

$$2\times 4\sqrt{3}$$

Multiply 2 and 4 to get 8.

$$8\sqrt{3}$$