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

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

Evaluate

$$18\sqrt{6}+1\approx 45.09081537$$

Solution Steps

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

$$8\left(\sqrt{2}\right)^{2}+20\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{2} is 2.

$$8\times 2+20\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

Multiply 8 and 2 to get 16.

$$16+20\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

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

$$16+20\sqrt{6}-2\sqrt{3}\sqrt{2}-5\left(\sqrt{3}\right)^{2}$$

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

$$16+20\sqrt{6}-2\sqrt{6}-5\left(\sqrt{3}\right)^{2}$$

Combine 20\sqrt{6} and -2\sqrt{6} to get 18\sqrt{6}.

$$16+18\sqrt{6}-5\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$16+18\sqrt{6}-5\times 3$$

Multiply -5 and 3 to get -15.

$$16+18\sqrt{6}-15$$

Subtract 15 from 16 to get 1.

$$1+18\sqrt{6}$$