Solve 3sqrt{1/18}*sqrt{1/8}divfrac{sqrt{2}}{4}

$$3 \sqrt { \frac { 1 } { 18 } } \times \sqrt { \frac { 1 } { 8 } } \div \frac { \sqrt { 2 } } { 4 }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

To multiply \sqrt{\frac{1}{18}} and \sqrt{\frac{1}{8}}, multiply the numbers under the square root.

$$\frac{3\sqrt{\frac{1}{144}}}{\frac{\sqrt{2}}{4}}$$

Rewrite the square root of the division \frac{1}{144} as the division of square roots \frac{\sqrt{1}}{\sqrt{144}}. Take the square root of both numerator and denominator.

$$\frac{3\times \frac{1}{12}}{\frac{\sqrt{2}}{4}}$$

Multiply 3 and \frac{1}{12} to get \frac{3}{12}.

$$\frac{\frac{3}{12}}{\frac{\sqrt{2}}{4}}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{4}}{\frac{\sqrt{2}}{4}}$$

Divide \frac{1}{4} by \frac{\sqrt{2}}{4} by multiplying \frac{1}{4} by the reciprocal of \frac{\sqrt{2}}{4}.

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

Rationalize the denominator of \frac{4}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Cancel out 4 in both numerator and denominator.

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