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

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

Evaluate

$$6\sqrt{6}+15\approx 29.696938457$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

Multiply 3 and 3 to get 9.

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

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

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

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

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

Combine 3\sqrt{6} and 3\sqrt{6} to get 6\sqrt{6}.

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

The square of \sqrt{2} is 2.

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

Multiply 3 and 2 to get 6.

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

Add 9 and 6 to get 15.

$$15+6\sqrt{6}$$

Factor

$$3 {(2 \sqrt{6} + 5)} = 29.696938457$$