Solve (3+1/4)^2-2/3:1/4+sqrt[3]{1-19/27}=

$$( 3 + \frac { 1 } { 4 } ) ^ { 2 } - \frac { 2 } { 3 } : \frac { 1 } { 4 } + \sqrt[ 3 ] { 1 - \frac { 19 } { 27 } } =$$

Evaluate

$$\frac{137}{16}=8.5625$$

Solution Steps

Add 3 and \frac{1}{4} to get \frac{13}{4}.

$$\left(\frac{13}{4}\right)^{2}-\frac{\frac{2}{3}}{\frac{1}{4}}+\sqrt[3]{1-\frac{19}{27}}$$

Calculate \frac{13}{4} to the power of 2 and get \frac{169}{16}.

$$\frac{169}{16}-\frac{\frac{2}{3}}{\frac{1}{4}}+\sqrt[3]{1-\frac{19}{27}}$$

Divide \frac{2}{3} by \frac{1}{4} by multiplying \frac{2}{3} by the reciprocal of \frac{1}{4}.

$$\frac{169}{16}-\frac{2}{3}\times 4+\sqrt[3]{1-\frac{19}{27}}$$

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

$$\frac{169}{16}-\frac{8}{3}+\sqrt[3]{1-\frac{19}{27}}$$

Subtract \frac{8}{3} from \frac{169}{16} to get \frac{379}{48}.

$$\frac{379}{48}+\sqrt[3]{1-\frac{19}{27}}$$

Subtract \frac{19}{27} from 1 to get \frac{8}{27}.

$$\frac{379}{48}+\sqrt[3]{\frac{8}{27}}$$

Calculate \sqrt[3]{\frac{8}{27}} and get \frac{2}{3}.

$$\frac{379}{48}+\frac{2}{3}$$

Add \frac{379}{48} and \frac{2}{3} to get \frac{137}{16}.

$$\frac{137}{16}$$

Factor

$$\frac{137}{2 ^ {4}} = 8\frac{9}{16} = 8.5625$$