Solve 5/600sqrt{36/16+9}:sqrt{64*50*2/64:4*9}=

$$\frac { 5 } { 600 } \sqrt { \frac { 36 } { 16 + 9 } } : \sqrt { \frac { 64 \cdot 50 \cdot 2 } { 64 : 4 \cdot 9 } } =$$

Evaluate

$$\frac{3}{2000}=0.0015$$

Solution Steps

Reduce the fraction \frac{5}{600} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{1}{120}\sqrt{\frac{36}{16+9}}}{\sqrt{\frac{64\times 50\times 2}{\frac{64}{4}\times 9}}}$$

Add 16 and 9 to get 25.

$$\frac{\frac{1}{120}\sqrt{\frac{36}{25}}}{\sqrt{\frac{64\times 50\times 2}{\frac{64}{4}\times 9}}}$$

Rewrite the square root of the division \frac{36}{25} as the division of square roots \frac{\sqrt{36}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1}{120}\times \frac{6}{5}}{\sqrt{\frac{64\times 50\times 2}{\frac{64}{4}\times 9}}}$$

Multiply \frac{1}{120} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 6}{120\times 5}}{\sqrt{\frac{64\times 50\times 2}{\frac{64}{4}\times 9}}}$$

Do the multiplications in the fraction \frac{1\times 6}{120\times 5}.

$$\frac{\frac{6}{600}}{\sqrt{\frac{64\times 50\times 2}{\frac{64}{4}\times 9}}}$$

Reduce the fraction \frac{6}{600} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{1}{100}}{\sqrt{\frac{64\times 50\times 2}{\frac{64}{4}\times 9}}}$$

Multiply 64 and 50 to get 3200.

$$\frac{\frac{1}{100}}{\sqrt{\frac{3200\times 2}{\frac{64}{4}\times 9}}}$$

Multiply 3200 and 2 to get 6400.

$$\frac{\frac{1}{100}}{\sqrt{\frac{6400}{\frac{64}{4}\times 9}}}$$

Divide 64 by 4 to get 16.

$$\frac{\frac{1}{100}}{\sqrt{\frac{6400}{16\times 9}}}$$

Multiply 16 and 9 to get 144.

$$\frac{\frac{1}{100}}{\sqrt{\frac{6400}{144}}}$$

Reduce the fraction \frac{6400}{144} to lowest terms by extracting and canceling out 16.

$$\frac{\frac{1}{100}}{\sqrt{\frac{400}{9}}}$$

Rewrite the square root of the division \frac{400}{9} as the division of square roots \frac{\sqrt{400}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1}{100}}{\frac{20}{3}}$$

Divide \frac{1}{100} by \frac{20}{3} by multiplying \frac{1}{100} by the reciprocal of \frac{20}{3}.

$$\frac{1}{100}\times \frac{3}{20}$$

Multiply \frac{1}{100} times \frac{3}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{100\times 20}$$

Do the multiplications in the fraction \frac{1\times 3}{100\times 20}.

$$\frac{3}{2000}$$

Factor

$$\frac{3}{2 ^ {4} \cdot 5 ^ {3}} = 0.0015$$