Solve 3/2-sqrt{{left(-3/2right)}^2-2}

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

Evaluate

$$1$$

Solution Steps

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{3}{2}-\sqrt{\frac{9}{4}-2}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{3}{2}-\sqrt{\frac{9}{4}-\frac{8}{4}}$$

Since \frac{9}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}-\sqrt{\frac{9-8}{4}}$$

Subtract 8 from 9 to get 1.

$$\frac{3}{2}-\sqrt{\frac{1}{4}}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

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

Since \frac{3}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 3 to get 2.

$$\frac{2}{2}$$

Divide 2 by 2 to get 1.

$$1$$

Factor

$$1$$