Solve sqrt{343/27}

$$\sqrt { \frac { 343 } { 27 } }$$

Evaluate

$$\frac{7\sqrt{21}}{9}\approx 3.564225541$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{343}{27}} as the division of square roots \frac{\sqrt{343}}{\sqrt{27}}.

$$\frac{\sqrt{343}}{\sqrt{27}}$$

Factor 343=7^{2}\times 7. Rewrite the square root of the product \sqrt{7^{2}\times 7} as the product of square roots \sqrt{7^{2}}\sqrt{7}. Take the square root of 7^{2}.

$$\frac{7\sqrt{7}}{\sqrt{27}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

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

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

The square of \sqrt{3} is 3.

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

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

$$\frac{7\sqrt{21}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{7\sqrt{21}}{9}$$