Solve (sqrt{6}+5)^2-(sqrt{6}+5)

$$( \sqrt { 6 } + 5 ) ^ { 2 } - ( \sqrt { 6 } + 5 )$$

Evaluate

$$9\sqrt{6}+26\approx 48.045407685$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{6}+5\right)^{2}.

$$\left(\sqrt{6}\right)^{2}+10\sqrt{6}+25-\left(\sqrt{6}+5\right)$$

The square of \sqrt{6} is 6.

$$6+10\sqrt{6}+25-\left(\sqrt{6}+5\right)$$

Add 6 and 25 to get 31.

$$31+10\sqrt{6}-\left(\sqrt{6}+5\right)$$

To find the opposite of \sqrt{6}+5, find the opposite of each term.

$$31+10\sqrt{6}-\sqrt{6}-5$$

Combine 10\sqrt{6} and -\sqrt{6} to get 9\sqrt{6}.

$$31+9\sqrt{6}-5$$

Subtract 5 from 31 to get 26.

$$26+9\sqrt{6}$$

Factor

$$9 \sqrt{6} + 26 = 48.045407685$$