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

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

Evaluate

$$-20\sqrt{21}-40\approx -131.651513899$$

Solution Steps

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

$$3\left(\sqrt{3}\right)^{2}-21\sqrt{3}\sqrt{7}+\sqrt{7}\sqrt{3}-7\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{3} is 3.

$$3\times 3-21\sqrt{3}\sqrt{7}+\sqrt{7}\sqrt{3}-7\left(\sqrt{7}\right)^{2}$$

Multiply 3 and 3 to get 9.

$$9-21\sqrt{3}\sqrt{7}+\sqrt{7}\sqrt{3}-7\left(\sqrt{7}\right)^{2}$$

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

$$9-21\sqrt{21}+\sqrt{7}\sqrt{3}-7\left(\sqrt{7}\right)^{2}$$

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

$$9-21\sqrt{21}+\sqrt{21}-7\left(\sqrt{7}\right)^{2}$$

Combine -21\sqrt{21} and \sqrt{21} to get -20\sqrt{21}.

$$9-20\sqrt{21}-7\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$9-20\sqrt{21}-7\times 7$$

Multiply -7 and 7 to get -49.

$$9-20\sqrt{21}-49$$

Subtract 49 from 9 to get -40.

$$-40-20\sqrt{21}$$