Solve 1/3/sqrt{8/3}

$$\frac{ \frac{ 1 }{ 3 } }{ \frac{ \sqrt{ 8 } }{ 3 } }$$

Evaluate

$$\frac{\sqrt{2}}{4}\approx 0.353553391$$

Solution Steps

Divide \frac{1}{3} by \frac{\sqrt{8}}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{\sqrt{8}}{3}.

$$\frac{3}{3\sqrt{8}}$$

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}.

$$\frac{3}{3\times 2\sqrt{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{3}{6\sqrt{2}}$$

Rationalize the denominator of \frac{3}{6\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{6\times 2}$$

Cancel out 3 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

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