Solve 5/6-[(2/5)^1*(5/2)^2-sqrt{9/16}*frac{1}{2}]+3=

$$\frac { 5 } { 6 } - [ ( \frac { 2 } { 5 } ) ^ { 1 } \times ( \frac { 5 } { 2 } ) ^ { 2 } - \sqrt { \frac { 9 } { 16 } } \times \frac { 1 } { 2 } ] + 3 =$$

Evaluate

$$\frac{41}{24}\approx 1.708333333$$

Solution Steps

Calculate \frac{2}{5} to the power of 1 and get \frac{2}{5}.

$$\frac{5}{6}-\left(\frac{2}{5}\times \left(\frac{5}{2}\right)^{2}-\sqrt{\frac{9}{16}}\times \frac{1}{2}\right)+3$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{5}{6}-\left(\frac{2}{5}\times \frac{25}{4}-\sqrt{\frac{9}{16}}\times \frac{1}{2}\right)+3$$

Multiply \frac{2}{5} times \frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{6}-\left(\frac{2\times 25}{5\times 4}-\sqrt{\frac{9}{16}}\times \frac{1}{2}\right)+3$$

Do the multiplications in the fraction \frac{2\times 25}{5\times 4}.

$$\frac{5}{6}-\left(\frac{50}{20}-\sqrt{\frac{9}{16}}\times \frac{1}{2}\right)+3$$

Reduce the fraction \frac{50}{20} to lowest terms by extracting and canceling out 10.

$$\frac{5}{6}-\left(\frac{5}{2}-\sqrt{\frac{9}{16}}\times \frac{1}{2}\right)+3$$

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.

$$\frac{5}{6}-\left(\frac{5}{2}-\frac{3}{4}\times \frac{1}{2}\right)+3$$

Multiply \frac{3}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{6}-\left(\frac{5}{2}-\frac{3\times 1}{4\times 2}\right)+3$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 2}.

$$\frac{5}{6}-\left(\frac{5}{2}-\frac{3}{8}\right)+3$$

Least common multiple of 2 and 8 is 8. Convert \frac{5}{2} and \frac{3}{8} to fractions with denominator 8.

$$\frac{5}{6}-\left(\frac{20}{8}-\frac{3}{8}\right)+3$$

Since \frac{20}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}-\frac{20-3}{8}+3$$

Subtract 3 from 20 to get 17.

$$\frac{5}{6}-\frac{17}{8}+3$$

Least common multiple of 6 and 8 is 24. Convert \frac{5}{6} and \frac{17}{8} to fractions with denominator 24.

$$\frac{20}{24}-\frac{51}{24}+3$$

Since \frac{20}{24} and \frac{51}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-51}{24}+3$$

Subtract 51 from 20 to get -31.

$$-\frac{31}{24}+3$$

Convert 3 to fraction \frac{72}{24}.

$$-\frac{31}{24}+\frac{72}{24}$$

Since -\frac{31}{24} and \frac{72}{24} have the same denominator, add them by adding their numerators.

$$\frac{-31+72}{24}$$

Add -31 and 72 to get 41.

$$\frac{41}{24}$$

Factor

$$\frac{41}{2 ^ {3} \cdot 3} = 1\frac{17}{24} = 1.7083333333333333$$