Solve frac{sqrt{left(2*2right)^2+{left(2*sqrt{13}right)}^2-5^2}}{2}

$$\frac{ \sqrt{ { \left(2 \times 2 \right) }^{ 2 } + { \left(2 \times \sqrt{ 13 } \right) }^{ 2 } - { 5 }^{ 2 } } }{ 2 }$$

Evaluate

$$\frac{\sqrt{43}}{2}\approx 3.278719262$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{4^{2}+\left(2\sqrt{13}\right)^{2}-5^{2}}}{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\sqrt{16+\left(2\sqrt{13}\right)^{2}-5^{2}}}{2}$$

Expand \left(2\sqrt{13}\right)^{2}.

$$\frac{\sqrt{16+2^{2}\left(\sqrt{13}\right)^{2}-5^{2}}}{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\sqrt{16+4\left(\sqrt{13}\right)^{2}-5^{2}}}{2}$$

The square of \sqrt{13} is 13.

$$\frac{\sqrt{16+4\times 13-5^{2}}}{2}$$

Multiply 4 and 13 to get 52.

$$\frac{\sqrt{16+52-5^{2}}}{2}$$

Add 16 and 52 to get 68.

$$\frac{\sqrt{68-5^{2}}}{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\sqrt{68-25}}{2}$$

Subtract 25 from 68 to get 43.

$$\frac{\sqrt{43}}{2}$$