Solve (3sqrt{5}+2sqrt{3})*(6sqrt{5}-4sqrt{3})=

$$( 3 \sqrt { 5 } + 2 \sqrt { 3 } ) \cdot ( 6 \sqrt { 5 } - 4 \sqrt { 3 } ) =$$

Evaluate

$$66$$

Solution Steps

Apply the distributive property by multiplying each term of 3\sqrt{5}+2\sqrt{3} by each term of 6\sqrt{5}-4\sqrt{3}.

$$18\left(\sqrt{5}\right)^{2}-12\sqrt{3}\sqrt{5}+12\sqrt{3}\sqrt{5}-8\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{5} is 5.

$$18\times 5-12\sqrt{3}\sqrt{5}+12\sqrt{3}\sqrt{5}-8\left(\sqrt{3}\right)^{2}$$

Multiply 18 and 5 to get 90.

$$90-12\sqrt{3}\sqrt{5}+12\sqrt{3}\sqrt{5}-8\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$90-12\sqrt{15}+12\sqrt{3}\sqrt{5}-8\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$90-12\sqrt{15}+12\sqrt{15}-8\left(\sqrt{3}\right)^{2}$$

Combine -12\sqrt{15} and 12\sqrt{15} to get 0.

$$90-8\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$90-8\times 3$$

Multiply -8 and 3 to get -24.

$$90-24$$

Subtract 24 from 90 to get 66.

$$66$$

Factor

$$2\times 3\times 11$$