Solve sqrt{4/3}*sqrt{7/3}*sqrt{7/5}

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

Evaluate

$$\frac{14\sqrt{5}}{15}\approx 2.086996779$$

Solution Steps

To multiply \sqrt{\frac{4}{3}} and \sqrt{\frac{7}{3}}, multiply the numbers under the square root.

$$\sqrt{\frac{28}{9}}\sqrt{\frac{7}{5}}$$

To multiply \sqrt{\frac{28}{9}} and \sqrt{\frac{7}{5}}, multiply the numbers under the square root.

$$\sqrt{\frac{196}{45}}$$

Rewrite the square root of the division \sqrt{\frac{196}{45}} as the division of square roots \frac{\sqrt{196}}{\sqrt{45}}.

$$\frac{\sqrt{196}}{\sqrt{45}}$$

Calculate the square root of 196 and get 14.

$$\frac{14}{\sqrt{45}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

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

Rationalize the denominator of \frac{14}{3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{14\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

Multiply 3 and 5 to get 15.

$$\frac{14\sqrt{5}}{15}$$