Solve (frac{sqrt{21}+5}{2})^2

$$( \frac { \sqrt { 21 } + 5 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{5\sqrt{21}+23}{2}\approx 22.956439237$$

Solution Steps

To raise \frac{\sqrt{21}+5}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{21}+5\right)^{2}}{2^{2}}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{21}+5\right)^{2}.

$$\frac{\left(\sqrt{21}\right)^{2}+10\sqrt{21}+25}{2^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{21+10\sqrt{21}+25}{2^{2}}$$

Add 21 and 25 to get 46.

$$\frac{46+10\sqrt{21}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{46+10\sqrt{21}}{4}$$

Expand

$$\frac{5 \sqrt{21} + 23}{2} = 22.9564392373896$$

Solution Steps

To raise \frac{\sqrt{21}+5}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{21}+5\right)^{2}}{2^{2}}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{21}+5\right)^{2}.

$$\frac{\left(\sqrt{21}\right)^{2}+10\sqrt{21}+25}{2^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{21+10\sqrt{21}+25}{2^{2}}$$

Add 21 and 25 to get 46.

$$\frac{46+10\sqrt{21}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{46+10\sqrt{21}}{4}$$