Solve (3sqrt{2}+sqrt{5})*(sqrt{2}-3sqrt{5})

$$( 3 \sqrt { 2 } + \sqrt { 5 } ) \cdot ( \sqrt { 2 } - 3 \sqrt { 5 } )$$

Evaluate

$$-8\sqrt{10}-9\approx -34.298221281$$

Solution Steps

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

$$3\left(\sqrt{2}\right)^{2}-9\sqrt{2}\sqrt{5}+\sqrt{5}\sqrt{2}-3\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{2} is 2.

$$3\times 2-9\sqrt{2}\sqrt{5}+\sqrt{5}\sqrt{2}-3\left(\sqrt{5}\right)^{2}$$

Multiply 3 and 2 to get 6.

$$6-9\sqrt{2}\sqrt{5}+\sqrt{5}\sqrt{2}-3\left(\sqrt{5}\right)^{2}$$

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

$$6-9\sqrt{10}+\sqrt{5}\sqrt{2}-3\left(\sqrt{5}\right)^{2}$$

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

$$6-9\sqrt{10}+\sqrt{10}-3\left(\sqrt{5}\right)^{2}$$

Combine -9\sqrt{10} and \sqrt{10} to get -8\sqrt{10}.

$$6-8\sqrt{10}-3\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$6-8\sqrt{10}-3\times 5$$

Multiply -3 and 5 to get -15.

$$6-8\sqrt{10}-15$$

Subtract 15 from 6 to get -9.

$$-9-8\sqrt{10}$$