Solve sqrt{left(5/2+5/4right)left(1/2-1/3right)-frac{1}{16}}

$$\sqrt{ \left( \frac{ 5 }{ 2 } + \frac{ 5 }{ 4 } \right) \left( \frac{ 1 }{ 2 } - \frac{ 1 }{ 3 } \right) - \frac{ 1 }{ 16 } }$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{5}{4} to fractions with denominator 4.

$$\sqrt{\left(\frac{10}{4}+\frac{5}{4}\right)\left(\frac{1}{2}-\frac{1}{3}\right)-\frac{1}{16}}$$

Since \frac{10}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{10+5}{4}\left(\frac{1}{2}-\frac{1}{3}\right)-\frac{1}{16}}$$

Add 10 and 5 to get 15.

$$\sqrt{\frac{15}{4}\left(\frac{1}{2}-\frac{1}{3}\right)-\frac{1}{16}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\sqrt{\frac{15}{4}\left(\frac{3}{6}-\frac{2}{6}\right)-\frac{1}{16}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{15}{4}\times \frac{3-2}{6}-\frac{1}{16}}$$

Subtract 2 from 3 to get 1.

$$\sqrt{\frac{15}{4}\times \frac{1}{6}-\frac{1}{16}}$$

Multiply \frac{15}{4} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{15\times 1}{4\times 6}-\frac{1}{16}}$$

Do the multiplications in the fraction \frac{15\times 1}{4\times 6}.

$$\sqrt{\frac{15}{24}-\frac{1}{16}}$$

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{5}{8}-\frac{1}{16}}$$

Least common multiple of 8 and 16 is 16. Convert \frac{5}{8} and \frac{1}{16} to fractions with denominator 16.

$$\sqrt{\frac{10}{16}-\frac{1}{16}}$$

Since \frac{10}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{10-1}{16}}$$

Subtract 1 from 10 to get 9.

$$\sqrt{\frac{9}{16}}$$

Rewrite the square root of the division \frac{9}{16} as the division of square roots \frac{\sqrt{9}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$