Solve sqrt{192/17}

$$\sqrt { \frac { 192 } { 17 } }$$

Evaluate

$$\frac{8\sqrt{51}}{17}\approx 3.360672202$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{192}{17}} as the division of square roots \frac{\sqrt{192}}{\sqrt{17}}.

$$\frac{\sqrt{192}}{\sqrt{17}}$$

Factor 192=8^{2}\times 3. Rewrite the square root of the product \sqrt{8^{2}\times 3} as the product of square roots \sqrt{8^{2}}\sqrt{3}. Take the square root of 8^{2}.

$$\frac{8\sqrt{3}}{\sqrt{17}}$$

Rationalize the denominator of \frac{8\sqrt{3}}{\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{8\sqrt{3}\sqrt{17}}{\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{8\sqrt{3}\sqrt{17}}{17}$$

To multiply \sqrt{3} and \sqrt{17}, multiply the numbers under the square root.

$$\frac{8\sqrt{51}}{17}$$