Solve (sqrt{5}+1)^2-10/sqrt{5}

$$( \sqrt { 5 } + 1 ) ^ { 2 } - \frac { 10 } { \sqrt { 5 } }$$

Evaluate

$$6$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{5}+1\right)^{2}.

$$\left(\sqrt{5}\right)^{2}+2\sqrt{5}+1-\frac{10}{\sqrt{5}}$$

The square of \sqrt{5} is 5.

$$5+2\sqrt{5}+1-\frac{10}{\sqrt{5}}$$

Add 5 and 1 to get 6.

$$6+2\sqrt{5}-\frac{10}{\sqrt{5}}$$

Rationalize the denominator of \frac{10}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

$$6+2\sqrt{5}-\frac{10\sqrt{5}}{5}$$

Divide 10\sqrt{5} by 5 to get 2\sqrt{5}.

$$6+2\sqrt{5}-2\sqrt{5}$$

Subtract 2\sqrt{5} from 2\sqrt{5} to get 0.

$$6$$

Factor

$$2\times 3$$