Solve (-sqrt{2})^2+sqrt[4]{1/81}+sqrt[3]{0.008}-sqrt[5]{-1/32}

$$( - \sqrt { 2 } ) ^ { 2 } + \sqrt[ 4 ] { \frac { 1 } { 81 } } + \sqrt[ 3 ] { 0.008 } - \sqrt[ 5 ] { - \frac { 1 } { 32 } }$$

Evaluate

$$\frac{91}{30}\approx 3.033333333$$

Solution Steps

Calculate -\sqrt{2} to the power of 2 and get \left(\sqrt{2}\right)^{2}.

$$\left(\sqrt{2}\right)^{2}+\sqrt[4]{\frac{1}{81}}+\sqrt[3]{0.008}-\sqrt[5]{-\frac{1}{32}}$$

Calculate \sqrt[4]{\frac{1}{81}} and get \frac{1}{3}.

$$\left(\sqrt{2}\right)^{2}+\frac{1}{3}+\sqrt[3]{0.008}-\sqrt[5]{-\frac{1}{32}}$$

Calculate \sqrt[3]{0.008} and get \frac{1}{5}.

$$\left(\sqrt{2}\right)^{2}+\frac{1}{3}+\frac{1}{5}-\sqrt[5]{-\frac{1}{32}}$$

Add \frac{1}{3} and \frac{1}{5} to get \frac{8}{15}.

$$\left(\sqrt{2}\right)^{2}+\frac{8}{15}-\sqrt[5]{-\frac{1}{32}}$$

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

$$\left(\sqrt{2}\right)^{2}+\frac{8}{15}-\left(-\frac{1}{2}\right)$$

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

$$\left(\sqrt{2}\right)^{2}+\frac{8}{15}+\frac{1}{2}$$

The square of \sqrt{2} is 2.

$$2+\frac{8}{15}+\frac{1}{2}$$

Add 2 and \frac{8}{15} to get \frac{38}{15}.

$$\frac{38}{15}+\frac{1}{2}$$

Add \frac{38}{15} and \frac{1}{2} to get \frac{91}{30}.

$$\frac{91}{30}$$

Factor

$$\frac{7 \cdot 13}{2 \cdot 3 \cdot 5} = 3\frac{1}{30} = 3.033333333333333$$