Solve 3sqrt{20}*sqrt{2/5}

$$3 \sqrt { 20 } \times \sqrt { \frac { 2 } { 5 } }$$

Evaluate

$$6\sqrt{2}\approx 8.485281374$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

Multiply 3 and 2 to get 6.

$$6\sqrt{5}\sqrt{\frac{2}{5}}$$

Rewrite the square root of the division \sqrt{\frac{2}{5}} as the division of square roots \frac{\sqrt{2}}{\sqrt{5}}.

$$6\sqrt{5}\times \frac{\sqrt{2}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$6\sqrt{5}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$6\sqrt{5}\times \frac{\sqrt{2}\sqrt{5}}{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$6\sqrt{5}\times \frac{\sqrt{10}}{5}$$

Express 6\times \frac{\sqrt{10}}{5} as a single fraction.

$$\frac{6\sqrt{10}}{5}\sqrt{5}$$

Express \frac{6\sqrt{10}}{5}\sqrt{5} as a single fraction.

$$\frac{6\sqrt{10}\sqrt{5}}{5}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\frac{6\sqrt{5}\sqrt{2}\sqrt{5}}{5}$$

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

$$\frac{6\times 5\sqrt{2}}{5}$$

Multiply 6 and 5 to get 30.

$$\frac{30\sqrt{2}}{5}$$

Divide 30\sqrt{2} by 5 to get 6\sqrt{2}.

$$6\sqrt{2}$$