Solve =frac{10sqrt{6}}{sqrt{7}}*frac{sqrt{2}}{sqrt{5}}

$$= \frac { 10 \sqrt { 6 } } { \sqrt { 7 } } \cdot \frac { \sqrt { 2 } } { \sqrt { 5 } }$$

Evaluate

$$\frac{4\sqrt{105}}{7}\approx 5.855400438$$

Solution Steps

Rationalize the denominator of \frac{10\sqrt{6}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{10\sqrt{6}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\times \frac{\sqrt{2}}{\sqrt{5}}$$

The square of \sqrt{7} is 7.

$$\frac{10\sqrt{6}\sqrt{7}}{7}\times \frac{\sqrt{2}}{\sqrt{5}}$$

To multiply \sqrt{6} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{10\sqrt{42}}{7}\times \frac{\sqrt{2}}{\sqrt{5}}$$

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

$$\frac{10\sqrt{42}}{7}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{10\sqrt{42}}{7}\times \frac{\sqrt{2}\sqrt{5}}{5}$$

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

$$\frac{10\sqrt{42}}{7}\times \frac{\sqrt{10}}{5}$$

Multiply \frac{10\sqrt{42}}{7} times \frac{\sqrt{10}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\sqrt{42}\sqrt{10}}{7\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2\sqrt{10}\sqrt{42}}{7}$$

To multiply \sqrt{10} and \sqrt{42}, multiply the numbers under the square root.

$$\frac{2\sqrt{420}}{7}$$

Factor 420=2^{2}\times 105. Rewrite the square root of the product \sqrt{2^{2}\times 105} as the product of square roots \sqrt{2^{2}}\sqrt{105}. Take the square root of 2^{2}.

$$\frac{2\times 2\sqrt{105}}{7}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{105}}{7}$$