Solve (sqrt{1/16+9/25-3/10})

$$( \sqrt { \frac { 1 } { 16 } + \frac { 9 } { 25 } - \frac { 3 } { 10 } } )$$

Evaluate

$$\frac{7}{20}=0.35$$

Solution Steps

Least common multiple of 16 and 25 is 400. Convert \frac{1}{16} and \frac{9}{25} to fractions with denominator 400.

$$\sqrt{\frac{25}{400}+\frac{144}{400}-\frac{3}{10}}$$

Since \frac{25}{400} and \frac{144}{400} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{25+144}{400}-\frac{3}{10}}$$

Add 25 and 144 to get 169.

$$\sqrt{\frac{169}{400}-\frac{3}{10}}$$

Least common multiple of 400 and 10 is 400. Convert \frac{169}{400} and \frac{3}{10} to fractions with denominator 400.

$$\sqrt{\frac{169}{400}-\frac{120}{400}}$$

Since \frac{169}{400} and \frac{120}{400} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{169-120}{400}}$$

Subtract 120 from 169 to get 49.

$$\sqrt{\frac{49}{400}}$$

Rewrite the square root of the division \frac{49}{400} as the division of square roots \frac{\sqrt{49}}{\sqrt{400}}. Take the square root of both numerator and denominator.

$$\frac{7}{20}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 5} = 0.35$$