Solve sqrt{49}*sqrt{1/3}

$$\sqrt { 49 } \times \sqrt { \frac { 1 } { 3 } }$$

Evaluate

$$\frac{7\sqrt{3}}{3}\approx 4.041451884$$

Solution Steps

Calculate the square root of 49 and get 7.

$$7\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$7\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$7\times \frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Express 7\times \frac{\sqrt{3}}{3} as a single fraction.

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