Solve (sqrt{3}+sqrt{10})(sqrt{3}-2sqrt{10})

$$( \sqrt { 3 } + \sqrt { 10 } ) ( \sqrt { 3 } - 2 \sqrt { 10 } )$$

Evaluate

$$-\sqrt{30}-17\approx -22.477225575$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{3}+\sqrt{10} by each term of \sqrt{3}-2\sqrt{10}.

$$\left(\sqrt{3}\right)^{2}-2\sqrt{3}\sqrt{10}+\sqrt{10}\sqrt{3}-2\left(\sqrt{10}\right)^{2}$$

The square of \sqrt{3} is 3.

$$3-2\sqrt{3}\sqrt{10}+\sqrt{10}\sqrt{3}-2\left(\sqrt{10}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$3-2\sqrt{30}+\sqrt{10}\sqrt{3}-2\left(\sqrt{10}\right)^{2}$$

To multiply \sqrt{10} and \sqrt{3}, multiply the numbers under the square root.

$$3-2\sqrt{30}+\sqrt{30}-2\left(\sqrt{10}\right)^{2}$$

Combine -2\sqrt{30} and \sqrt{30} to get -\sqrt{30}.

$$3-\sqrt{30}-2\left(\sqrt{10}\right)^{2}$$

The square of \sqrt{10} is 10.

$$3-\sqrt{30}-2\times 10$$

Multiply -2 and 10 to get -20.

$$3-\sqrt{30}-20$$

Subtract 20 from 3 to get -17.

$$-17-\sqrt{30}$$