Solve sqrt{8}*sqrt{1/36}divsqrt{41/2}

$$\sqrt { 8 } \cdot \sqrt { \frac { 1 } { 36 } } \div \sqrt { 4 \frac { 1 } { 2 } }$$

Evaluate

$$\frac{2}{9}\approx 0.222222222$$

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}.

$$\frac{2\sqrt{2}\sqrt{\frac{1}{36}}}{\sqrt{\frac{4\times 2+1}{2}}}$$

Rewrite the square root of the division \frac{1}{36} as the division of square roots \frac{\sqrt{1}}{\sqrt{36}}. Take the square root of both numerator and denominator.

$$\frac{2\sqrt{2}\times \frac{1}{6}}{\sqrt{\frac{4\times 2+1}{2}}}$$

Multiply 2 and \frac{1}{6} to get \frac{2}{6}.

$$\frac{\frac{2}{6}\sqrt{2}}{\sqrt{\frac{4\times 2+1}{2}}}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Multiply 4 and 2 to get 8.

$$\frac{\frac{1}{3}\sqrt{2}}{\sqrt{\frac{8+1}{2}}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{1}{3}\sqrt{2}}{\sqrt{\frac{9}{2}}}$$

Rewrite the square root of the division \sqrt{\frac{9}{2}} as the division of square roots \frac{\sqrt{9}}{\sqrt{2}}.

$$\frac{\frac{1}{3}\sqrt{2}}{\frac{\sqrt{9}}{\sqrt{2}}}$$

Calculate the square root of 9 and get 3.

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

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

$$\frac{\frac{1}{3}\sqrt{2}}{\frac{3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

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

Divide \frac{1}{3}\sqrt{2} by \frac{3\sqrt{2}}{2} by multiplying \frac{1}{3}\sqrt{2} by the reciprocal of \frac{3\sqrt{2}}{2}.

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

Cancel out \sqrt{2} in both numerator and denominator.

$$\frac{\frac{1}{3}\times 2}{3}$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{\frac{2}{3}}{3}$$

Express \frac{\frac{2}{3}}{3} as a single fraction.

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

Multiply 3 and 3 to get 9.

$$\frac{2}{9}$$

Factor

$$\frac{2}{3 ^ {2}} = 0.2222222222222222$$