Solve 3sqrt{7/2}

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

Evaluate

$$\frac{3\sqrt{14}}{2}\approx 5.61248608$$

Solution Steps

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

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Express 3\times \frac{\sqrt{14}}{2} as a single fraction.

$$\frac{3\sqrt{14}}{2}$$