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

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

Evaluate

$$11\sqrt{6}-30\approx -3.055612829$$

Solution Steps

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

$$30\left(\sqrt{2}\right)^{2}-25\sqrt{3}\sqrt{2}+36\sqrt{3}\sqrt{2}-30\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{2} is 2.

$$30\times 2-25\sqrt{3}\sqrt{2}+36\sqrt{3}\sqrt{2}-30\left(\sqrt{3}\right)^{2}$$

Multiply 30 and 2 to get 60.

$$60-25\sqrt{3}\sqrt{2}+36\sqrt{3}\sqrt{2}-30\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$60-25\sqrt{6}+36\sqrt{3}\sqrt{2}-30\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$60-25\sqrt{6}+36\sqrt{6}-30\left(\sqrt{3}\right)^{2}$$

Combine -25\sqrt{6} and 36\sqrt{6} to get 11\sqrt{6}.

$$60+11\sqrt{6}-30\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$60+11\sqrt{6}-30\times 3$$

Multiply -30 and 3 to get -90.

$$60+11\sqrt{6}-90$$

Subtract 90 from 60 to get -30.

$$-30+11\sqrt{6}$$