Solve -6sqrt{3/17}

$$-6 \sqrt{ \frac{ 3 }{ 17 } }$$

Evaluate

$$-\frac{6\sqrt{51}}{17}\approx -2.520504151$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{17}} as the division of square roots \frac{\sqrt{3}}{\sqrt{17}}.

$$-6\times \frac{\sqrt{3}}{\sqrt{17}}$$

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

$$-6\times \frac{\sqrt{3}\sqrt{17}}{\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$-6\times \frac{\sqrt{3}\sqrt{17}}{17}$$

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

$$-6\times \frac{\sqrt{51}}{17}$$

Express -6\times \frac{\sqrt{51}}{17} as a single fraction.

$$\frac{-6\sqrt{51}}{17}$$