Solve sqrt[2]{3^-1+6^-1/8^-1}

$$\sqrt[ 2 ]{ \frac{ { 3 }^{ -1 } + { 6 }^{ -1 } }{ { 8 }^{ -1 } } }$$

Evaluate

$$2$$

Solution Steps

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\sqrt[2]{\frac{\frac{1}{3}+6^{-1}}{8^{-1}}}$$

Calculate 6 to the power of -1 and get \frac{1}{6}.

$$\sqrt[2]{\frac{\frac{1}{3}+\frac{1}{6}}{8^{-1}}}$$

Add \frac{1}{3} and \frac{1}{6} to get \frac{1}{2}.

$$\sqrt[2]{\frac{\frac{1}{2}}{8^{-1}}}$$

Calculate 8 to the power of -1 and get \frac{1}{8}.

$$\sqrt[2]{\frac{\frac{1}{2}}{\frac{1}{8}}}$$

Divide \frac{1}{2} by \frac{1}{8} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{8}.

$$\sqrt[2]{\frac{1}{2}\times 8}$$

Multiply \frac{1}{2} and 8 to get 4.

$$\sqrt[2]{4}$$

Calculate \sqrt[2]{4} and get 2.

$$2$$

Factor

$$2$$