Solve sqrt{1/16-1/25}:sqrt{1/36+1/64}

$$\sqrt { \frac { 1 } { 16 } - \frac { 1 } { 25 } } : \sqrt { \frac { 1 } { 36 } + \frac { 1 } { 64 } }$$

Evaluate

$$\frac{18}{25}=0.72$$

Solution Steps

Least common multiple of 16 and 25 is 400. Convert \frac{1}{16} and \frac{1}{25} to fractions with denominator 400.

$$\frac{\sqrt{\frac{25}{400}-\frac{16}{400}}}{\sqrt{\frac{1}{36}+\frac{1}{64}}}$$

Since \frac{25}{400} and \frac{16}{400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{\frac{25-16}{400}}}{\sqrt{\frac{1}{36}+\frac{1}{64}}}$$

Subtract 16 from 25 to get 9.

$$\frac{\sqrt{\frac{9}{400}}}{\sqrt{\frac{1}{36}+\frac{1}{64}}}$$

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

$$\frac{\frac{3}{20}}{\sqrt{\frac{1}{36}+\frac{1}{64}}}$$

Least common multiple of 36 and 64 is 576. Convert \frac{1}{36} and \frac{1}{64} to fractions with denominator 576.

$$\frac{\frac{3}{20}}{\sqrt{\frac{16}{576}+\frac{9}{576}}}$$

Since \frac{16}{576} and \frac{9}{576} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{20}}{\sqrt{\frac{16+9}{576}}}$$

Add 16 and 9 to get 25.

$$\frac{\frac{3}{20}}{\sqrt{\frac{25}{576}}}$$

Rewrite the square root of the division \frac{25}{576} as the division of square roots \frac{\sqrt{25}}{\sqrt{576}}. Take the square root of both numerator and denominator.

$$\frac{\frac{3}{20}}{\frac{5}{24}}$$

Divide \frac{3}{20} by \frac{5}{24} by multiplying \frac{3}{20} by the reciprocal of \frac{5}{24}.

$$\frac{3}{20}\times \frac{24}{5}$$

Multiply \frac{3}{20} times \frac{24}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 24}{20\times 5}$$

Do the multiplications in the fraction \frac{3\times 24}{20\times 5}.

$$\frac{72}{100}$$

Reduce the fraction \frac{72}{100} to lowest terms by extracting and canceling out 4.

$$\frac{18}{25}$$

Factor

$$\frac{2 \cdot 3 ^ {2}}{5 ^ {2}} = 0.72$$