Solve 7sqrt{2}+6sqrt[3]{5}-8sqrt{2}+7sqrt{4}-sqrt[3]{-1}-sqrt[4]{16}+sqrt[3]{5}-24

$$7 \sqrt { 2 } + 6 \sqrt[ 3 ] { 5 } - 8 \sqrt { 2 } + 7 \sqrt { 4 } - \sqrt[ 3 ] { - 1 } - \sqrt[ 4 ] { 16 } + \sqrt[ 3 ] { 5 } - 24$$

Evaluate

$$7\sqrt[3]{5}-\sqrt{2}-11\approx -0.444381936$$

Solution Steps

Combine 7\sqrt{2} and -8\sqrt{2} to get -\sqrt{2}.

$$-\sqrt{2}+6\sqrt[3]{5}+7\sqrt{4}-\sqrt[3]{-1}-\sqrt[4]{16}+\sqrt[3]{5}-24$$

Calculate the square root of 4 and get 2.

$$-\sqrt{2}+6\sqrt[3]{5}+7\times 2-\sqrt[3]{-1}-\sqrt[4]{16}+\sqrt[3]{5}-24$$

Multiply 7 and 2 to get 14.

$$-\sqrt{2}+6\sqrt[3]{5}+14-\sqrt[3]{-1}-\sqrt[4]{16}+\sqrt[3]{5}-24$$

Calculate \sqrt[3]{-1} and get -1.

$$-\sqrt{2}+6\sqrt[3]{5}+14-\left(-1\right)-\sqrt[4]{16}+\sqrt[3]{5}-24$$

The opposite of -1 is 1.

$$-\sqrt{2}+6\sqrt[3]{5}+14+1-\sqrt[4]{16}+\sqrt[3]{5}-24$$

Calculate \sqrt[4]{16} and get 2.

$$-\sqrt{2}+6\sqrt[3]{5}+14+1-2+\sqrt[3]{5}-24$$

Add 14 and 1 to get 15.

$$-\sqrt{2}+6\sqrt[3]{5}+15-2+\sqrt[3]{5}-24$$

Subtract 2 from 15 to get 13.

$$-\sqrt{2}+6\sqrt[3]{5}+13+\sqrt[3]{5}-24$$

Combine 6\sqrt[3]{5} and \sqrt[3]{5} to get 7\sqrt[3]{5}.

$$-\sqrt{2}+7\sqrt[3]{5}+13-24$$

Subtract 24 from 13 to get -11.

$$-\sqrt{2}+7\sqrt[3]{5}-11$$