Solve frac{{left(2sqrt{7}-4right)}^2}{}+(frac{2sqrt{7}+4}{2}

$$\frac{ { \left(2 \sqrt{ 7 } -4 \right) }^{ 2 } }{ } +( \frac{ 2 \sqrt{ 7 } +4 }{ 2 }$$

Evaluate

$$46-15\sqrt{7}\approx 6.313730334$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2\sqrt{7}-4\right)^{2}.

$$\frac{4\left(\sqrt{7}\right)^{2}-16\sqrt{7}+16}{1}+\frac{2\sqrt{7}+4}{2}$$

The square of \sqrt{7} is 7.

$$\frac{4\times 7-16\sqrt{7}+16}{1}+\frac{2\sqrt{7}+4}{2}$$

Multiply 4 and 7 to get 28.

$$\frac{28-16\sqrt{7}+16}{1}+\frac{2\sqrt{7}+4}{2}$$

Add 28 and 16 to get 44.

$$\frac{44-16\sqrt{7}}{1}+\frac{2\sqrt{7}+4}{2}$$

Anything divided by one gives itself.

$$44-16\sqrt{7}+\frac{2\sqrt{7}+4}{2}$$

Divide each term of 2\sqrt{7}+4 by 2 to get \sqrt{7}+2.

$$44-16\sqrt{7}+\sqrt{7}+2$$

Combine -16\sqrt{7} and \sqrt{7} to get -15\sqrt{7}.

$$44-15\sqrt{7}+2$$

Add 44 and 2 to get 46.

$$46-15\sqrt{7}$$