Solve 1/8sqrt{96}

$$\frac { 1 } { 8 } \sqrt { 96 }$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$\frac{1}{8}\times 4\sqrt{6}$$

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

$$\frac{4}{8}\sqrt{6}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{1}{2}\sqrt{6}$$