Solve 0.5/sqrt{8}

$$\frac { 0.5 } { \sqrt { 8 } }$$

Evaluate

$$\frac{\sqrt{2}}{8}\approx 0.176776695$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{0.5}{2\sqrt{2}}$$

Rationalize the denominator of \frac{0.5}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{0.5\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{0.5\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{0.5\sqrt{2}}{4}$$

Divide 0.5\sqrt{2} by 4 to get 0.125\sqrt{2}.

$$0.125\sqrt{2}$$