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

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

Evaluate

$$2-11\sqrt{6}\approx -24.944387171$$

Solution Steps

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

$$10\left(\sqrt{2}\right)^{2}+4\sqrt{3}\sqrt{2}-15\sqrt{3}\sqrt{2}-6\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{2} is 2.

$$10\times 2+4\sqrt{3}\sqrt{2}-15\sqrt{3}\sqrt{2}-6\left(\sqrt{3}\right)^{2}$$

Multiply 10 and 2 to get 20.

$$20+4\sqrt{3}\sqrt{2}-15\sqrt{3}\sqrt{2}-6\left(\sqrt{3}\right)^{2}$$

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

$$20+4\sqrt{6}-15\sqrt{3}\sqrt{2}-6\left(\sqrt{3}\right)^{2}$$

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

$$20+4\sqrt{6}-15\sqrt{6}-6\left(\sqrt{3}\right)^{2}$$

Combine 4\sqrt{6} and -15\sqrt{6} to get -11\sqrt{6}.

$$20-11\sqrt{6}-6\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$20-11\sqrt{6}-6\times 3$$

Multiply -6 and 3 to get -18.

$$20-11\sqrt{6}-18$$

Subtract 18 from 20 to get 2.

$$2-11\sqrt{6}$$

Factor

$$2-11\sqrt{6}$$