Solve {l}{sqrt{(-5)^2}-sqrt[3]{-155/8}+sqrt{51/16}}{-1}

$$\left. \begin{array} { l } { \sqrt { ( - 5 ) ^ { 2 } } - \sqrt[ 3 ] { - 15 \frac { 5 } { 8 } } + \sqrt { 5 \frac { 1 } { 16 } } } \\ { - 1 } \end{array} \right.$$

Evaluate

$$\frac{35}{4}=8.75$$

Solution Steps

Calculate -5 to the power of 2 and get 25.

$$\sqrt{25}-\sqrt[3]{-\frac{15\times 8+5}{8}}+\sqrt{\frac{5\times 16+1}{16}}-1$$

Calculate the square root of 25 and get 5.

$$5-\sqrt[3]{-\frac{15\times 8+5}{8}}+\sqrt{\frac{5\times 16+1}{16}}-1$$

Multiply 15 and 8 to get 120.

$$5-\sqrt[3]{-\frac{120+5}{8}}+\sqrt{\frac{5\times 16+1}{16}}-1$$

Add 120 and 5 to get 125.

$$5-\sqrt[3]{-\frac{125}{8}}+\sqrt{\frac{5\times 16+1}{16}}-1$$

Calculate \sqrt[3]{-\frac{125}{8}} and get -\frac{5}{2}.

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

The opposite of -\frac{5}{2} is \frac{5}{2}.

$$5+\frac{5}{2}+\sqrt{\frac{5\times 16+1}{16}}-1$$

Add 5 and \frac{5}{2} to get \frac{15}{2}.

$$\frac{15}{2}+\sqrt{\frac{5\times 16+1}{16}}-1$$

Multiply 5 and 16 to get 80.

$$\frac{15}{2}+\sqrt{\frac{80+1}{16}}-1$$

Add 80 and 1 to get 81.

$$\frac{15}{2}+\sqrt{\frac{81}{16}}-1$$

Rewrite the square root of the division \frac{81}{16} as the division of square roots \frac{\sqrt{81}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{15}{2}+\frac{9}{4}-1$$

Add \frac{15}{2} and \frac{9}{4} to get \frac{39}{4}.

$$\frac{39}{4}-1$$

Subtract 1 from \frac{39}{4} to get \frac{35}{4}.

$$\frac{35}{4}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {2}} = 8\frac{3}{4} = 8.75$$