Solve sqrt{[(4-15/4)^2+(1/2)^2]:[(1-5/8):3/2+(2-frac{3}{2})]*(4^2-1)}

$$\sqrt { [ ( 4 - \frac { 15 } { 4 } ) ^ { 2 } + ( \frac { 1 } { 2 } ) ^ { 2 } ] : [ ( 1 - \frac { 5 } { 8 } ) : \frac { 3 } { 2 } + ( 2 - \frac { 3 } { 2 } ) ] \times ( 4 ^ { 2 } - 1 ) }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Subtract \frac{15}{4} from 4 to get \frac{1}{4}.

$$\sqrt{\frac{\left(\frac{1}{4}\right)^{2}+\left(\frac{1}{2}\right)^{2}}{\frac{1-\frac{5}{8}}{\frac{3}{2}}+2-\frac{3}{2}}\left(4^{2}-1\right)}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\sqrt{\frac{\frac{1}{16}+\left(\frac{1}{2}\right)^{2}}{\frac{1-\frac{5}{8}}{\frac{3}{2}}+2-\frac{3}{2}}\left(4^{2}-1\right)}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\sqrt{\frac{\frac{1}{16}+\frac{1}{4}}{\frac{1-\frac{5}{8}}{\frac{3}{2}}+2-\frac{3}{2}}\left(4^{2}-1\right)}$$

Add \frac{1}{16} and \frac{1}{4} to get \frac{5}{16}.

$$\sqrt{\frac{\frac{5}{16}}{\frac{1-\frac{5}{8}}{\frac{3}{2}}+2-\frac{3}{2}}\left(4^{2}-1\right)}$$

Subtract \frac{5}{8} from 1 to get \frac{3}{8}.

$$\sqrt{\frac{\frac{5}{16}}{\frac{\frac{3}{8}}{\frac{3}{2}}+2-\frac{3}{2}}\left(4^{2}-1\right)}$$

Divide \frac{3}{8} by \frac{3}{2} by multiplying \frac{3}{8} by the reciprocal of \frac{3}{2}.

$$\sqrt{\frac{\frac{5}{16}}{\frac{3}{8}\times \frac{2}{3}+2-\frac{3}{2}}\left(4^{2}-1\right)}$$

Multiply \frac{3}{8} and \frac{2}{3} to get \frac{1}{4}.

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

Add \frac{1}{4} and 2 to get \frac{9}{4}.

$$\sqrt{\frac{\frac{5}{16}}{\frac{9}{4}-\frac{3}{2}}\left(4^{2}-1\right)}$$

Subtract \frac{3}{2} from \frac{9}{4} to get \frac{3}{4}.

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

Divide \frac{5}{16} by \frac{3}{4} by multiplying \frac{5}{16} by the reciprocal of \frac{3}{4}.

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

Multiply \frac{5}{16} and \frac{4}{3} to get \frac{5}{12}.

$$\sqrt{\frac{5}{12}\left(4^{2}-1\right)}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{\frac{5}{12}\left(16-1\right)}$$

Subtract 1 from 16 to get 15.

$$\sqrt{\frac{5}{12}\times 15}$$

Multiply \frac{5}{12} and 15 to get \frac{25}{4}.

$$\sqrt{\frac{25}{4}}$$

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$