Solve (sqrt{5}+sqrt{3})(sqrt{5}+sqrt{3})

$$( \sqrt{ 5 } + \sqrt{ 3 } )( \sqrt{ 5 } + \sqrt{ 3 } )$$

Evaluate

$$2\left(\sqrt{15}+4\right)\approx 15.745966692$$

Solution Steps

Multiply \sqrt{5}+\sqrt{3} and \sqrt{5}+\sqrt{3} to get \left(\sqrt{5}+\sqrt{3}\right)^{2}.

$$\left(\sqrt{5}+\sqrt{3}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{5}+\sqrt{3}\right)^{2}.

$$\left(\sqrt{5}\right)^{2}+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{5} is 5.

$$5+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$5+2\sqrt{15}+\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$5+2\sqrt{15}+3$$

Add 5 and 3 to get 8.

$$8+2\sqrt{15}$$

Factor

$$2 {(\sqrt{15} + 4)} = 15.745966692$$