Solve frac{2sqrt{14}*3sqrt{7}}{sqrt{20}}

$$\frac { 2 \sqrt { 14 } \times 3 \sqrt { 7 } } { \sqrt { 20 } }$$

Evaluate

$$\frac{21\sqrt{10}}{5}\approx 13.281566173$$

Solution Steps

Factor 14=7\times 2. Rewrite the square root of the product \sqrt{7\times 2} as the product of square roots \sqrt{7}\sqrt{2}.

$$\frac{2\times 3\sqrt{7}\sqrt{2}\sqrt{7}}{\sqrt{20}}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{2\times 3\times 7\sqrt{2}}{\sqrt{20}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\times 7\sqrt{2}}{\sqrt{20}}$$

Multiply 6 and 7 to get 42.

$$\frac{42\sqrt{2}}{\sqrt{20}}$$

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}.

$$\frac{42\sqrt{2}}{2\sqrt{5}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{21\sqrt{2}}{\sqrt{5}}$$

Rationalize the denominator of \frac{21\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{21\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{21\sqrt{2}\sqrt{5}}{5}$$

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

$$\frac{21\sqrt{10}}{5}$$