Solve 7/5*sqrt{4/3}

$$\frac { 7 } { 5 } \times \sqrt { \frac { 4 } { 3 } }$$

Evaluate

$$\frac{14\sqrt{3}}{15}\approx 1.616580754$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{4}{3}} as the division of square roots \frac{\sqrt{4}}{\sqrt{3}}.

$$\frac{7}{5}\times \frac{\sqrt{4}}{\sqrt{3}}$$

Calculate the square root of 4 and get 2.

$$\frac{7}{5}\times \frac{2}{\sqrt{3}}$$

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

$$\frac{7}{5}\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{7}{5}\times \frac{2\sqrt{3}}{3}$$

Multiply \frac{7}{5} times \frac{2\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 2\sqrt{3}}{5\times 3}$$

Multiply 7 and 2 to get 14.

$$\frac{14\sqrt{3}}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{14\sqrt{3}}{15}$$