Solve -14-15/sqrt{58*27}=

$$\frac{ -14-15 }{ \sqrt{ 58 \cdot 27 } } =$$

Evaluate

$$-\frac{\sqrt{174}}{18}\approx -0.732828109$$

Solution Steps

Subtract 15 from -14 to get -29.

$$\frac{-29}{\sqrt{58\times 27}}$$

Multiply 58 and 27 to get 1566.

$$\frac{-29}{\sqrt{1566}}$$

Factor 1566=3^{2}\times 174. Rewrite the square root of the product \sqrt{3^{2}\times 174} as the product of square roots \sqrt{3^{2}}\sqrt{174}. Take the square root of 3^{2}.

$$\frac{-29}{3\sqrt{174}}$$

Rationalize the denominator of \frac{-29}{3\sqrt{174}} by multiplying numerator and denominator by \sqrt{174}.

$$\frac{-29\sqrt{174}}{3\left(\sqrt{174}\right)^{2}}$$

The square of \sqrt{174} is 174.

$$\frac{-29\sqrt{174}}{3\times 174}$$

Cancel out 29 in both numerator and denominator.

$$\frac{-\sqrt{174}}{3\times 6}$$

Multiply 3 and 6 to get 18.

$$\frac{-\sqrt{174}}{18}$$