Solve frac{sqrt{2}sqrt{18}}{sqrt{25/100}+sqrt[3]{1/1000}}

$$\frac{ \sqrt{ 2 } \sqrt{ 18 } }{ \sqrt{ \frac{ 25 }{ 100 } } + \sqrt[ 3 ]{ \frac{ 1 }{ 1000 } } }$$

Evaluate

$$10$$

Solution Steps

Factor 18=2\times 9. Rewrite the square root of the product \sqrt{2\times 9} as the product of square roots \sqrt{2}\sqrt{9}.

$$\frac{\sqrt{2}\sqrt{2}\sqrt{9}}{\sqrt{\frac{25}{100}}+\sqrt[3]{\frac{1}{1000}}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{2\sqrt{9}}{\sqrt{\frac{25}{100}}+\sqrt[3]{\frac{1}{1000}}}$$

Calculate the square root of 9 and get 3.

$$\frac{2\times 3}{\sqrt{\frac{25}{100}}+\sqrt[3]{\frac{1}{1000}}}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{\sqrt{\frac{25}{100}}+\sqrt[3]{\frac{1}{1000}}}$$

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{6}{\sqrt{\frac{1}{4}}+\sqrt[3]{\frac{1}{1000}}}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{6}{\frac{1}{2}+\sqrt[3]{\frac{1}{1000}}}$$

Calculate \sqrt[3]{\frac{1}{1000}} and get \frac{1}{10}.

$$\frac{6}{\frac{1}{2}+\frac{1}{10}}$$

Add \frac{1}{2} and \frac{1}{10} to get \frac{3}{5}.

$$\frac{6}{\frac{3}{5}}$$

Divide 6 by \frac{3}{5} by multiplying 6 by the reciprocal of \frac{3}{5}.

$$6\times \frac{5}{3}$$

Multiply 6 and \frac{5}{3} to get 10.

$$10$$

Factor

$$2\times 5$$