Solve (6sqrt{3}+9sqrt{10})(4sqrt{3}-7sqrt{10})

$$( 6 \sqrt { 3 } + 9 \sqrt { 10 } ) ( 4 \sqrt { 3 } - 7 \sqrt { 10 } )$$

Evaluate

$$-6\sqrt{30}-558\approx -590.86335345$$

Solution Steps

Apply the distributive property by multiplying each term of 6\sqrt{3}+9\sqrt{10} by each term of 4\sqrt{3}-7\sqrt{10}.

$$24\left(\sqrt{3}\right)^{2}-42\sqrt{3}\sqrt{10}+36\sqrt{3}\sqrt{10}-63\left(\sqrt{10}\right)^{2}$$

The square of \sqrt{3} is 3.

$$24\times 3-42\sqrt{3}\sqrt{10}+36\sqrt{3}\sqrt{10}-63\left(\sqrt{10}\right)^{2}$$

Multiply 24 and 3 to get 72.

$$72-42\sqrt{3}\sqrt{10}+36\sqrt{3}\sqrt{10}-63\left(\sqrt{10}\right)^{2}$$

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

$$72-42\sqrt{30}+36\sqrt{3}\sqrt{10}-63\left(\sqrt{10}\right)^{2}$$

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

$$72-42\sqrt{30}+36\sqrt{30}-63\left(\sqrt{10}\right)^{2}$$

Combine -42\sqrt{30} and 36\sqrt{30} to get -6\sqrt{30}.

$$72-6\sqrt{30}-63\left(\sqrt{10}\right)^{2}$$

The square of \sqrt{10} is 10.

$$72-6\sqrt{30}-63\times 10$$

Multiply -63 and 10 to get -630.

$$72-6\sqrt{30}-630$$

Subtract 630 from 72 to get -558.

$$-558-6\sqrt{30}$$

Factor

$$6 {(-\sqrt{30} - 93)} = -590.86335345$$