Solve sqrt{9}-sqrt[3]{-8}-(3sqrt{2}-51-2(1/sqrt{2}+sqrt{2})=

$$\sqrt { 9 } - \sqrt[ 3 ] { - 8 } - ( 3 \sqrt { 2 } - 51 - 2 ( \frac { 1 } { \sqrt { 2 } } + \sqrt { 2 } ) =$$

Evaluate

$$56$$

Solution Steps

Calculate the square root of 9 and get 3.

$$3-\sqrt[3]{-8}-\left(3\sqrt{2}-51-2\left(\frac{1}{\sqrt{2}}+\sqrt{2}\right)\right)$$

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

$$3-\left(-2\right)-\left(3\sqrt{2}-51-2\left(\frac{1}{\sqrt{2}}+\sqrt{2}\right)\right)$$

The opposite of -2 is 2.

$$3+2-\left(3\sqrt{2}-51-2\left(\frac{1}{\sqrt{2}}+\sqrt{2}\right)\right)$$

Add 3 and 2 to get 5.

$$5-\left(3\sqrt{2}-51-2\left(\frac{1}{\sqrt{2}}+\sqrt{2}\right)\right)$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$5-\left(3\sqrt{2}-51-2\left(\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\sqrt{2}\right)\right)$$

The square of \sqrt{2} is 2.

$$5-\left(3\sqrt{2}-51-2\left(\frac{\sqrt{2}}{2}+\sqrt{2}\right)\right)$$

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

$$5-\left(3\sqrt{2}-51-2\times \frac{3}{2}\sqrt{2}\right)$$

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

$$5-\left(3\sqrt{2}-51-3\sqrt{2}\right)$$

Combine 3\sqrt{2} and -3\sqrt{2} to get 0.

$$5-\left(-51\right)$$

The opposite of -51 is 51.

$$5+51$$

Add 5 and 51 to get 56.

$$56$$

Factor

$$2^{3}\times 7$$