Solve sqrt[2005]{-1}+pi^0-sqrt[3]{8}+|-5|-sqrt[5]{-1/32}

$$\sqrt[ 2005 ] { - 1 } + \pi ^ { 0 } - \sqrt[ 3 ] { 8 } + | - 5 | - \sqrt[ 5 ] { - \frac { 1 } { 32 } }$$

Evaluate

$$\frac{7}{2}=3.5$$

Solution Steps

Calculate \sqrt[2005]{-1} and get -1.

$$-1+\pi ^{0}-\sqrt[3]{8}+|-5|-\sqrt[5]{-\frac{1}{32}}$$

Calculate \pi to the power of 0 and get 1.

$$-1+1-\sqrt[3]{8}+|-5|-\sqrt[5]{-\frac{1}{32}}$$

Add -1 and 1 to get 0.

$$0-\sqrt[3]{8}+|-5|-\sqrt[5]{-\frac{1}{32}}$$

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

$$0-2+|-5|-\sqrt[5]{-\frac{1}{32}}$$

Subtract 2 from 0 to get -2.

$$-2+|-5|-\sqrt[5]{-\frac{1}{32}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -5 is 5.

$$-2+5-\sqrt[5]{-\frac{1}{32}}$$

Add -2 and 5 to get 3.

$$3-\sqrt[5]{-\frac{1}{32}}$$

Calculate \sqrt[5]{-\frac{1}{32}} and get -\frac{1}{2}.

$$3-\left(-\frac{1}{2}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$3+\frac{1}{2}$$

Add 3 and \frac{1}{2} to get \frac{7}{2}.

$$\frac{7}{2}$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$