Solve (sqrt{2}-sqrt{5})(-4sqrt{2}-3sqrt{5})

$$( \sqrt { 2 } - \sqrt { 5 } ) ( - 4 \sqrt { 2 } - 3 \sqrt { 5 } )$$

Evaluate

$$\sqrt{10}+7\approx 10.16227766$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{2}-\sqrt{5} by each term of -4\sqrt{2}-3\sqrt{5}.

$$-4\left(\sqrt{2}\right)^{2}-3\sqrt{2}\sqrt{5}+4\sqrt{5}\sqrt{2}+3\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{2} is 2.

$$-4\times 2-3\sqrt{2}\sqrt{5}+4\sqrt{5}\sqrt{2}+3\left(\sqrt{5}\right)^{2}$$

Multiply -4 and 2 to get -8.

$$-8-3\sqrt{2}\sqrt{5}+4\sqrt{5}\sqrt{2}+3\left(\sqrt{5}\right)^{2}$$

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

$$-8-3\sqrt{10}+4\sqrt{5}\sqrt{2}+3\left(\sqrt{5}\right)^{2}$$

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

$$-8-3\sqrt{10}+4\sqrt{10}+3\left(\sqrt{5}\right)^{2}$$

Combine -3\sqrt{10} and 4\sqrt{10} to get \sqrt{10}.

$$-8+\sqrt{10}+3\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$-8+\sqrt{10}+3\times 5$$

Multiply 3 and 5 to get 15.

$$-8+\sqrt{10}+15$$

Add -8 and 15 to get 7.

$$7+\sqrt{10}$$