Solve 7sqrt{2}-3sqrt[3]{3}-5sqrt{2}+7sqrt[3]{3}-1/2sqrt{2}

$$7 \sqrt { 2 } - 3 \sqrt[ 3 ] { 3 } - 5 \sqrt { 2 } + 7 \sqrt[ 3 ] { 3 } - \frac { 1 } { 2 } \sqrt { 2 }$$

Evaluate

$$\frac{3\sqrt{2}}{2}+4\sqrt[3]{3}\approx 7.890318625$$

Solution Steps

Combine 7\sqrt{2} and -5\sqrt{2} to get 2\sqrt{2}.

$$2\sqrt{2}-3\sqrt[3]{3}+7\sqrt[3]{3}-\frac{1}{2}\sqrt{2}$$

Combine -3\sqrt[3]{3} and 7\sqrt[3]{3} to get 4\sqrt[3]{3}.

$$2\sqrt{2}+4\sqrt[3]{3}-\frac{1}{2}\sqrt{2}$$

Combine 2\sqrt{2} and -\frac{1}{2}\sqrt{2} to get \frac{3}{2}\sqrt{2}.

$$\frac{3}{2}\sqrt{2}+4\sqrt[3]{3}$$

Factor

$$\frac{\sqrt[3]{3} {(\sqrt{2} \cdot 3 ^ {\frac{2}{3}} + 8)}}{2} = 7.890318624789276$$