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

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

Evaluate

$$2$$

Solution Steps

Multiply 2 and 1 to get 2.

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

Multiply 10 and 1 to get 10.

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

Subtract 10 from 2 to get -8.

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

Multiply 11 and -2 to get -22.

$$|\frac{-8-22}{\sqrt{2^{2}+\left(-10\right)^{2}+11^{2}}}|$$

Subtract 22 from -8 to get -30.

$$|\frac{-30}{\sqrt{2^{2}+\left(-10\right)^{2}+11^{2}}}|$$

Calculate 2 to the power of 2 and get 4.

$$|\frac{-30}{\sqrt{4+\left(-10\right)^{2}+11^{2}}}|$$

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

$$|\frac{-30}{\sqrt{4+100+11^{2}}}|$$

Add 4 and 100 to get 104.

$$|\frac{-30}{\sqrt{104+11^{2}}}|$$

Calculate 11 to the power of 2 and get 121.

$$|\frac{-30}{\sqrt{104+121}}|$$

Add 104 and 121 to get 225.

$$|\frac{-30}{\sqrt{225}}|$$

Calculate the square root of 225 and get 15.

$$|\frac{-30}{15}|$$

Divide -30 by 15 to get -2.

$$|-2|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$2$$

Factor

$$2$$