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

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

Evaluate

$$13\sqrt{6}+30\approx 61.843366656$$

Solution Steps

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

$$4\sqrt{3}\sqrt{2}+6\left(\sqrt{3}\right)^{2}+6\left(\sqrt{2}\right)^{2}+9\sqrt{3}\sqrt{2}$$

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

$$4\sqrt{6}+6\left(\sqrt{3}\right)^{2}+6\left(\sqrt{2}\right)^{2}+9\sqrt{3}\sqrt{2}$$

The square of \sqrt{3} is 3.

$$4\sqrt{6}+6\times 3+6\left(\sqrt{2}\right)^{2}+9\sqrt{3}\sqrt{2}$$

Multiply 6 and 3 to get 18.

$$4\sqrt{6}+18+6\left(\sqrt{2}\right)^{2}+9\sqrt{3}\sqrt{2}$$

The square of \sqrt{2} is 2.

$$4\sqrt{6}+18+6\times 2+9\sqrt{3}\sqrt{2}$$

Multiply 6 and 2 to get 12.

$$4\sqrt{6}+18+12+9\sqrt{3}\sqrt{2}$$

Add 18 and 12 to get 30.

$$4\sqrt{6}+30+9\sqrt{3}\sqrt{2}$$

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

$$4\sqrt{6}+30+9\sqrt{6}$$

Combine 4\sqrt{6} and 9\sqrt{6} to get 13\sqrt{6}.

$$13\sqrt{6}+30$$

Factor

$$13 \sqrt{6} + 30 = 61.843366656$$