Solve 1/4sqrt{18}*8sqrt{1/36}div(2/3sqrt{9/2})

$$\frac{ 1 }{ 4 } \sqrt{ 18 } \times 8 \sqrt{ \frac{ 1 }{ 36 } } \div ( \frac{ 2 }{ 3 } \sqrt{ \frac{ 9 }{ 2 } } )$$

Evaluate

$$1$$

Solution Steps

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

$$\frac{\frac{8}{4}\sqrt{18}\sqrt{\frac{1}{36}}}{\frac{2}{3}\sqrt{\frac{9}{2}}}$$

Divide 8 by 4 to get 2.

$$\frac{2\sqrt{18}\sqrt{\frac{1}{36}}}{\frac{2}{3}\sqrt{\frac{9}{2}}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{2\times 3\sqrt{2}\sqrt{\frac{1}{36}}}{\frac{2}{3}\sqrt{\frac{9}{2}}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{2}\sqrt{\frac{1}{36}}}{\frac{2}{3}\sqrt{\frac{9}{2}}}$$

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.

$$\frac{6\sqrt{2}\times \frac{1}{6}}{\frac{2}{3}\sqrt{\frac{9}{2}}}$$

Cancel out 6 and 6.

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

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

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

Calculate the square root of 9 and get 3.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply \frac{2}{3} times \frac{3\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2\times 3 in both numerator and denominator.

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

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

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$