Solve 4sqrt{5}divsqrt{48}*2sqrt{15}

$$4 \sqrt { 5 } \div \sqrt { 48 } \times 2 \sqrt { 15 }$$

Evaluate

$$10$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$2\times \frac{4\sqrt{5}}{4\sqrt{3}}\sqrt{15}$$

Cancel out 4 in both numerator and denominator.

$$2\times \frac{\sqrt{5}}{\sqrt{3}}\sqrt{15}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2\times \frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{15}$$

The square of \sqrt{3} is 3.

$$2\times \frac{\sqrt{5}\sqrt{3}}{3}\sqrt{15}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

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

Express 2\times \frac{\sqrt{15}}{3} as a single fraction.

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

Express \frac{2\sqrt{15}}{3}\sqrt{15} as a single fraction.

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

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$\frac{2\times 15}{3}$$

Multiply 2 and 15 to get 30.

$$\frac{30}{3}$$

Divide 30 by 3 to get 10.

$$10$$

Factor

$$2\times 5$$