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

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

Evaluate

$$\sqrt{14}+\sqrt{21}-\sqrt{6}-3\approx 2.874743339$$

Solution Steps

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

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

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

$$\sqrt{14}-\sqrt{2}\sqrt{3}+\sqrt{3}\sqrt{7}-\left(\sqrt{3}\right)^{2}$$

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

$$\sqrt{14}-\sqrt{6}+\sqrt{3}\sqrt{7}-\left(\sqrt{3}\right)^{2}$$

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

$$\sqrt{14}-\sqrt{6}+\sqrt{21}-\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$\sqrt{14}-\sqrt{6}+\sqrt{21}-3$$