Solve -7/2-sqrt{{left(-7/2right)}^2-6}

$$\frac{ -7 }{ 2 } - \sqrt{ { \left( \frac{ -7 }{ 2 } \right) }^{ 2 } -6 }$$

Evaluate

$$-6$$

Solution Steps

Fraction \frac{-7}{2} can be rewritten as -\frac{7}{2} by extracting the negative sign.

$$-\frac{7}{2}-\sqrt{\left(\frac{-7}{2}\right)^{2}-6}$$

Fraction \frac{-7}{2} can be rewritten as -\frac{7}{2} by extracting the negative sign.

$$-\frac{7}{2}-\sqrt{\left(-\frac{7}{2}\right)^{2}-6}$$

Calculate -\frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$-\frac{7}{2}-\sqrt{\frac{49}{4}-6}$$

Subtract 6 from \frac{49}{4} to get \frac{25}{4}.

$$-\frac{7}{2}-\sqrt{\frac{25}{4}}$$

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$-\frac{7}{2}-\frac{5}{2}$$

Subtract \frac{5}{2} from -\frac{7}{2} to get -6.

$$-6$$

Factor

$$-6$$