Solve sqrt{3}*sqrt{2/7}

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

Evaluate

$$\frac{\sqrt{42}}{7}\approx 0.9258201$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{7}} as the division of square roots \frac{\sqrt{2}}{\sqrt{7}}.

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

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\sqrt{3}\times \frac{\sqrt{2}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

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

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

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

Express \sqrt{3}\times \frac{\sqrt{14}}{7} as a single fraction.

$$\frac{\sqrt{3}\sqrt{14}}{7}$$

To multiply \sqrt{3} and \sqrt{14}, multiply the numbers under the square root.

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