Solve 7/2sqrt{2/3}

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

Evaluate

$$\frac{7\sqrt{6}}{6}\approx 2.857738033$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

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

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{7}{2}\times \frac{\sqrt{6}}{3}$$

Multiply \frac{7}{2} times \frac{\sqrt{6}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\sqrt{6}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{7\sqrt{6}}{6}$$