Solve (2)(sqrt{5}+sqrt{3})(sqrt{5}+2)

$$( 2 ) ( \sqrt { 5 } + \sqrt { 3 } ) ( \sqrt { 5 } + 2 )$$

Evaluate

$$2\left(\sqrt{15}+2\sqrt{3}+2\sqrt{5}+5\right)\approx 33.618441833$$

Solution Steps

Use the distributive property to multiply 2 by \sqrt{5}+\sqrt{3}.

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

Apply the distributive property by multiplying each term of 2\sqrt{5}+2\sqrt{3} by each term of \sqrt{5}+2.

$$2\left(\sqrt{5}\right)^{2}+4\sqrt{5}+2\sqrt{3}\sqrt{5}+4\sqrt{3}$$

The square of \sqrt{5} is 5.

$$2\times 5+4\sqrt{5}+2\sqrt{3}\sqrt{5}+4\sqrt{3}$$

Multiply 2 and 5 to get 10.

$$10+4\sqrt{5}+2\sqrt{3}\sqrt{5}+4\sqrt{3}$$

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

$$10+4\sqrt{5}+2\sqrt{15}+4\sqrt{3}$$