Solve sqrt{31/2}-2

$$\sqrt{ 3 \frac { 1 } { 2 } } -2$$

Evaluate

$$\frac{\sqrt{14}}{2}-2\approx -0.129171307$$

Short Solution Steps

Multiply 3 and 2 to get 6.

$$\sqrt{\frac{6+1}{2}}-2$$

Add 6 and 1 to get 7.

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

Rewrite the square root of the division \sqrt{\frac{7}{2}} as the division of square roots \frac{\sqrt{7}}{\sqrt{2}}.

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

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{7}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-2$$

The square of \sqrt{2} is 2.

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

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2}{2}.

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

Since \frac{\sqrt{14}}{2} and \frac{2\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \sqrt{14}-2\times 2.

$$\frac{\sqrt{14}-4}{2}$$