Solve -sqrt{12/17}

$$- \sqrt { \frac { 12 } { 17 } }$$

Evaluate

$$-\frac{2\sqrt{51}}{17}\approx -0.84016805$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{12}{17}} as the division of square roots \frac{\sqrt{12}}{\sqrt{17}}.

$$-\frac{\sqrt{12}}{\sqrt{17}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$-\frac{2\sqrt{3}}{\sqrt{17}}$$

Rationalize the denominator of \frac{2\sqrt{3}}{\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

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

The square of \sqrt{17} is 17.

$$-\frac{2\sqrt{3}\sqrt{17}}{17}$$

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

$$-\frac{2\sqrt{51}}{17}$$