Solve (-2*0-2*0+3*10/sqrt{(-2)^2+(-2)^2+3^2})=

$$( - \frac { 2 \cdot 0 - 2 \cdot 0 + 3 \cdot 10 } { \sqrt { ( - 2 ) ^ { 2 } + ( - 2 ) ^ { 2 } + 3 ^ { 2 } } } ) =$$

Evaluate

$$-\frac{30\sqrt{17}}{17}\approx -7.276068751$$

Solution Steps

Multiply 2 and 0 to get 0.

$$-\frac{0-2\times 0+3\times 10}{\sqrt{\left(-2\right)^{2}+\left(-2\right)^{2}+3^{2}}}$$

Multiply 2 and 0 to get 0.

$$-\frac{0-0+3\times 10}{\sqrt{\left(-2\right)^{2}+\left(-2\right)^{2}+3^{2}}}$$

Subtracting 0 from itself leaves 0.

$$-\frac{0+3\times 10}{\sqrt{\left(-2\right)^{2}+\left(-2\right)^{2}+3^{2}}}$$

Multiply 3 and 10 to get 30.

$$-\frac{0+30}{\sqrt{\left(-2\right)^{2}+\left(-2\right)^{2}+3^{2}}}$$

Add 0 and 30 to get 30.

$$-\frac{30}{\sqrt{\left(-2\right)^{2}+\left(-2\right)^{2}+3^{2}}}$$

Calculate -2 to the power of 2 and get 4.

$$-\frac{30}{\sqrt{4+\left(-2\right)^{2}+3^{2}}}$$

Calculate -2 to the power of 2 and get 4.

$$-\frac{30}{\sqrt{4+4+3^{2}}}$$

Add 4 and 4 to get 8.

$$-\frac{30}{\sqrt{8+3^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{30}{\sqrt{8+9}}$$

Add 8 and 9 to get 17.

$$-\frac{30}{\sqrt{17}}$$

Rationalize the denominator of \frac{30}{\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$-\frac{30\sqrt{17}}{\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$-\frac{30\sqrt{17}}{17}$$