Solve -(4)divsqrt{(4)^2-4+1(2)}

$$- ( 4 ) \div \sqrt { ( 4 ) ^ { 2 } - 4 + 1 ( 2 ) }$$

Evaluate

$$-\frac{2\sqrt{14}}{7}\approx -1.069044968$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{-4}{\sqrt{16-4+1\times 2}}$$

Subtract 4 from 16 to get 12.

$$\frac{-4}{\sqrt{12+1\times 2}}$$

Multiply 1 and 2 to get 2.

$$\frac{-4}{\sqrt{12+2}}$$

Add 12 and 2 to get 14.

$$\frac{-4}{\sqrt{14}}$$

Rationalize the denominator of \frac{-4}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

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

The square of \sqrt{14} is 14.

$$\frac{-4\sqrt{14}}{14}$$

Divide -4\sqrt{14} by 14 to get -\frac{2}{7}\sqrt{14}.

$$-\frac{2}{7}\sqrt{14}$$