Solve 3/4sqrt{28/3}

$$\frac { 3 } { 4 } \sqrt { \frac { 28 } { 3 } }$$

Evaluate

$$\frac{\sqrt{21}}{2}\approx 2.291287847$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{28}{3}} as the division of square roots \frac{\sqrt{28}}{\sqrt{3}}.

$$\frac{3}{4}\times \frac{\sqrt{28}}{\sqrt{3}}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{3}{4}\times \frac{2\sqrt{7}}{\sqrt{3}}$$

Rationalize the denominator of \frac{2\sqrt{7}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{3}{4}\times \frac{2\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{3}{4}\times \frac{2\sqrt{7}\sqrt{3}}{3}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{3}{4}\times \frac{2\sqrt{21}}{3}$$

Multiply \frac{3}{4} times \frac{2\sqrt{21}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2\sqrt{21}}{4\times 3}$$

Cancel out 2\times 3 in both numerator and denominator.

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