Solve 2*1-10*1+11*(-2)/sqrt{2^2+(-10)^2+1^2}

$$\frac { 2 \cdot 1 - 10 \cdot 1 + 11 \cdot ( - 2 ) } { \sqrt { 2 ^ { 2 } + ( - 10 ) ^ { 2 } + 1 ^ { 2 } } }$$

Evaluate

$$-\frac{2\sqrt{105}}{7}\approx -2.927700219$$

Solution Steps

Multiply 2 and 1 to get 2.

$$\frac{2-10\times 1+11\left(-2\right)}{\sqrt{2^{2}+\left(-10\right)^{2}+1^{2}}}$$

Multiply 10 and 1 to get 10.

$$\frac{2-10+11\left(-2\right)}{\sqrt{2^{2}+\left(-10\right)^{2}+1^{2}}}$$

Subtract 10 from 2 to get -8.

$$\frac{-8+11\left(-2\right)}{\sqrt{2^{2}+\left(-10\right)^{2}+1^{2}}}$$

Multiply 11 and -2 to get -22.

$$\frac{-8-22}{\sqrt{2^{2}+\left(-10\right)^{2}+1^{2}}}$$

Subtract 22 from -8 to get -30.

$$\frac{-30}{\sqrt{2^{2}+\left(-10\right)^{2}+1^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{-30}{\sqrt{4+\left(-10\right)^{2}+1^{2}}}$$

Calculate -10 to the power of 2 and get 100.

$$\frac{-30}{\sqrt{4+100+1^{2}}}$$

Add 4 and 100 to get 104.

$$\frac{-30}{\sqrt{104+1^{2}}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{-30}{\sqrt{104+1}}$$

Add 104 and 1 to get 105.

$$\frac{-30}{\sqrt{105}}$$

Rationalize the denominator of \frac{-30}{\sqrt{105}} by multiplying numerator and denominator by \sqrt{105}.

$$\frac{-30\sqrt{105}}{\left(\sqrt{105}\right)^{2}}$$

The square of \sqrt{105} is 105.

$$\frac{-30\sqrt{105}}{105}$$

Divide -30\sqrt{105} by 105 to get -\frac{2}{7}\sqrt{105}.

$$-\frac{2}{7}\sqrt{105}$$