Solve (sqrt{8}-sqrt{7})(sqrt{2}+sqrt{3})

$$( \sqrt { 8 } - \sqrt { 7 } ) ( \sqrt { 2 } + \sqrt { 3 } )$$

Evaluate

$$2\sqrt{6}+4-\sqrt{14}-\sqrt{21}\approx 0.574746404$$

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}.

$$\left(2\sqrt{2}-\sqrt{7}\right)\left(\sqrt{2}+\sqrt{3}\right)$$

Apply the distributive property by multiplying each term of 2\sqrt{2}-\sqrt{7} by each term of \sqrt{2}+\sqrt{3}.

$$2\left(\sqrt{2}\right)^{2}+2\sqrt{2}\sqrt{3}-\sqrt{7}\sqrt{2}-\sqrt{7}\sqrt{3}$$

The square of \sqrt{2} is 2.

$$2\times 2+2\sqrt{2}\sqrt{3}-\sqrt{7}\sqrt{2}-\sqrt{7}\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$4+2\sqrt{2}\sqrt{3}-\sqrt{7}\sqrt{2}-\sqrt{7}\sqrt{3}$$

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

$$4+2\sqrt{6}-\sqrt{7}\sqrt{2}-\sqrt{7}\sqrt{3}$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$4+2\sqrt{6}-\sqrt{14}-\sqrt{7}\sqrt{3}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$4+2\sqrt{6}-\sqrt{14}-\sqrt{21}$$