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

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

Evaluate

$$4\sqrt{3}+4-\sqrt{10}-\sqrt{30}\approx 2.288699995$$

Solution Steps

Apply the distributive property by multiplying each term of 2\sqrt{2}-\sqrt{5} by each term of \sqrt{2}+\sqrt{6}.

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

$$4+2\sqrt{2}\sqrt{6}-\sqrt{5}\sqrt{2}-\sqrt{5}\sqrt{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$4+2\sqrt{2}\sqrt{2}\sqrt{3}-\sqrt{5}\sqrt{2}-\sqrt{5}\sqrt{6}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$4+2\times 2\sqrt{3}-\sqrt{5}\sqrt{2}-\sqrt{5}\sqrt{6}$$

Multiply 2 and 2 to get 4.

$$4+4\sqrt{3}-\sqrt{5}\sqrt{2}-\sqrt{5}\sqrt{6}$$

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

$$4+4\sqrt{3}-\sqrt{10}-\sqrt{5}\sqrt{6}$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$4+4\sqrt{3}-\sqrt{10}-\sqrt{30}$$