Solve 2sqrt{16/31}=

$$2 \sqrt { \frac { 16 } { 31 } } =$$

Evaluate

$$\frac{8\sqrt{31}}{31}\approx 1.436842416$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{16}{31}} as the division of square roots \frac{\sqrt{16}}{\sqrt{31}}.

$$2\times \frac{\sqrt{16}}{\sqrt{31}}$$

Calculate the square root of 16 and get 4.

$$2\times \frac{4}{\sqrt{31}}$$

Rationalize the denominator of \frac{4}{\sqrt{31}} by multiplying numerator and denominator by \sqrt{31}.

$$2\times \frac{4\sqrt{31}}{\left(\sqrt{31}\right)^{2}}$$

The square of \sqrt{31} is 31.

$$2\times \frac{4\sqrt{31}}{31}$$

Express 2\times \frac{4\sqrt{31}}{31} as a single fraction.

$$\frac{2\times 4\sqrt{31}}{31}$$

Multiply 2 and 4 to get 8.

$$\frac{8\sqrt{31}}{31}$$