Solve {left(-sqrt{21/2}right)}^2

$${ \left(- \sqrt{ \frac{ 21 }{ 2 } } \right) }^{ 2 }$$

Evaluate

$$\frac{21}{2}=10.5$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{21}{2}} as the division of square roots \frac{\sqrt{21}}{\sqrt{2}}.

$$\left(-\frac{\sqrt{21}}{\sqrt{2}}\right)^{2}$$

Rationalize the denominator of \frac{\sqrt{21}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\left(-\frac{\sqrt{21}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)^{2}$$

The square of \sqrt{2} is 2.

$$\left(-\frac{\sqrt{21}\sqrt{2}}{2}\right)^{2}$$

To multiply \sqrt{21} and \sqrt{2}, multiply the numbers under the square root.

$$\left(-\frac{\sqrt{42}}{2}\right)^{2}$$

Calculate -\frac{\sqrt{42}}{2} to the power of 2 and get \left(\frac{\sqrt{42}}{2}\right)^{2}.

$$\left(\frac{\sqrt{42}}{2}\right)^{2}$$

To raise \frac{\sqrt{42}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{42}\right)^{2}}{2^{2}}$$

The square of \sqrt{42} is 42.

$$\frac{42}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{42}{4}$$

Reduce the fraction \frac{42}{4} to lowest terms by extracting and canceling out 2.

$$\frac{21}{2}$$

Factor

$$\frac{3 \cdot 7}{2} = 10\frac{1}{2} = 10.5$$