Solve |1-4+3-14|/sqrt{1+4+1}

$$\frac { | 1 - 4 + 3 - 14 | } { \sqrt { 1 + 4 + 1 } }$$

Evaluate

$$\frac{7\sqrt{6}}{3}\approx 5.715476066$$

Solution Steps

Subtract 4 from 1 to get -3.

$$\frac{|-3+3-14|}{\sqrt{1+4+1}}$$

Add -3 and 3 to get 0.

$$\frac{|-14|}{\sqrt{1+4+1}}$$

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.

$$\frac{14}{\sqrt{1+4+1}}$$

Add 1 and 4 to get 5.

$$\frac{14}{\sqrt{5+1}}$$

Add 5 and 1 to get 6.

$$\frac{14}{\sqrt{6}}$$

Rationalize the denominator of \frac{14}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

$$\frac{14\sqrt{6}}{6}$$

Divide 14\sqrt{6} by 6 to get \frac{7}{3}\sqrt{6}.

$$\frac{7}{3}\sqrt{6}$$