Solve (sqrt{8}+sqrt{2})(sqrt{5}+sqrt{3})

$$( \sqrt { 8 } + \sqrt { 2 } ) ( \sqrt { 5 } + \sqrt { 3 } )$$

Evaluate

$$3\sqrt{6}+3\sqrt{10}\approx 16.835302209$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Combine 2\sqrt{2} and \sqrt{2} to get 3\sqrt{2}.

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

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

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

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$3\sqrt{10}+3\sqrt{6}$$