Solve |2*1+3*2-6*3-4|/sqrt{2^2+3^2+(-6)^2}

$$\frac { | 2 \times 1 + 3 \times 2 - 6 \times 3 - 4 | } { \sqrt { 2 ^ { 2 } + 3 ^ { 2 } + ( - 6 ) ^ { 2 } } }$$

Evaluate

$$2$$

Solution Steps

Multiply 2 and 1 to get 2. Multiply 3 and 2 to get 6.

$$\frac{|2+6-6\times 3-4|}{\sqrt{2^{2}+3^{2}+\left(-6\right)^{2}}}$$

Add 2 and 6 to get 8.

$$\frac{|8-6\times 3-4|}{\sqrt{2^{2}+3^{2}+\left(-6\right)^{2}}}$$

Multiply 6 and 3 to get 18.

$$\frac{|8-18-4|}{\sqrt{2^{2}+3^{2}+\left(-6\right)^{2}}}$$

Subtract 18 from 8 to get -10.

$$\frac{|-10-4|}{\sqrt{2^{2}+3^{2}+\left(-6\right)^{2}}}$$

Subtract 4 from -10 to get -14.

$$\frac{|-14|}{\sqrt{2^{2}+3^{2}+\left(-6\right)^{2}}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -14 is 14.

$$\frac{14}{\sqrt{2^{2}+3^{2}+\left(-6\right)^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{14}{\sqrt{4+3^{2}+\left(-6\right)^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{14}{\sqrt{4+9+\left(-6\right)^{2}}}$$

Add 4 and 9 to get 13.

$$\frac{14}{\sqrt{13+\left(-6\right)^{2}}}$$

Calculate -6 to the power of 2 and get 36.

$$\frac{14}{\sqrt{13+36}}$$

Add 13 and 36 to get 49.

$$\frac{14}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{14}{7}$$

Divide 14 by 7 to get 2.

$$2$$

Factor

$$2$$