Solve frac{[5+(+sqrt{81})-20]-[-10+sqrt[3]{8}+12]}{sqrt{4}+sqrt[3]{8}}

$$\frac { [ 5 + ( + \sqrt { 81 } ) - 20 ] - [ - 10 + \sqrt[ 3 ] { 8 } + 12 ] } { \sqrt { 4 } + \sqrt[ 3 ] { 8 } }$$

Evaluate

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

Solution Steps

Calculate the square root of 81 and get 9.

$$\frac{5+9-20-\left(-10+\sqrt[3]{8}+12\right)}{\sqrt{4}+\sqrt[3]{8}}$$

Add 5 and 9 to get 14.

$$\frac{14-20-\left(-10+\sqrt[3]{8}+12\right)}{\sqrt{4}+\sqrt[3]{8}}$$

Subtract 20 from 14 to get -6.

$$\frac{-6-\left(-10+\sqrt[3]{8}+12\right)}{\sqrt{4}+\sqrt[3]{8}}$$

Calculate \sqrt[3]{8} and get 2.

$$\frac{-6-\left(-10+2+12\right)}{\sqrt{4}+\sqrt[3]{8}}$$

Add -10 and 2 to get -8.

$$\frac{-6-\left(-8+12\right)}{\sqrt{4}+\sqrt[3]{8}}$$

Add -8 and 12 to get 4.

$$\frac{-6-4}{\sqrt{4}+\sqrt[3]{8}}$$

Subtract 4 from -6 to get -10.

$$\frac{-10}{\sqrt{4}+\sqrt[3]{8}}$$

Calculate the square root of 4 and get 2.

$$\frac{-10}{2+\sqrt[3]{8}}$$

Calculate \sqrt[3]{8} and get 2.

$$\frac{-10}{2+2}$$

Add 2 and 2 to get 4.

$$\frac{-10}{4}$$

Reduce the fraction \frac{-10}{4} to lowest terms by extracting and canceling out 2.

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

Factor

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