Solve -2/sqrt{14*6}

$$\frac { - 2 } { \sqrt { 14 \times 6 } }$$

Evaluate

$$-\frac{\sqrt{21}}{21}\approx -0.21821789$$

Solution Steps

Multiply 14 and 6 to get 84.

$$\frac{-2}{\sqrt{84}}$$

Factor 84=2^{2}\times 21. Rewrite the square root of the product \sqrt{2^{2}\times 21} as the product of square roots \sqrt{2^{2}}\sqrt{21}. Take the square root of 2^{2}.

$$\frac{-2}{2\sqrt{21}}$$

Rationalize the denominator of \frac{-2}{2\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{-2\sqrt{21}}{2\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{-2\sqrt{21}}{2\times 21}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\sqrt{21}}{21}$$