Solve -46/sqrt{27sqrt{86}}

$$\frac{ -46 }{ \sqrt{ 27 } \sqrt{ 86 } }$$

Evaluate

$$-\frac{23\sqrt{258}}{387}\approx -0.954611636$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{-46}{3\sqrt{3}\sqrt{86}}$$

To multiply \sqrt{3} and \sqrt{86}, multiply the numbers under the square root.

$$\frac{-46}{3\sqrt{258}}$$

Rationalize the denominator of \frac{-46}{3\sqrt{258}} by multiplying numerator and denominator by \sqrt{258}.

$$\frac{-46\sqrt{258}}{3\left(\sqrt{258}\right)^{2}}$$

The square of \sqrt{258} is 258.

$$\frac{-46\sqrt{258}}{3\times 258}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-23\sqrt{258}}{3\times 129}$$

Multiply 3 and 129 to get 387.

$$\frac{-23\sqrt{258}}{387}$$