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

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

Evaluate

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

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

Multiply 6 and 3 to get 18.

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

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

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

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

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

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

$$18+13\sqrt{6}+6\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$18+13\sqrt{6}+6\times 2$$

Multiply 6 and 2 to get 12.

$$18+13\sqrt{6}+12$$

Add 18 and 12 to get 30.

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

Factor

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