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

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

Evaluate

$$15\sqrt{2}+24\approx 45.213203436$$

Solution Steps

Use the distributive property to multiply 3 by \sqrt{2}+3.

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

Apply the distributive property by multiplying each term of 3\sqrt{2}+9 by each term of \sqrt{2}+2.

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

The square of \sqrt{2} is 2.

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

Multiply 3 and 2 to get 6.

$$6+6\sqrt{2}+9\sqrt{2}+18$$

Combine 6\sqrt{2} and 9\sqrt{2} to get 15\sqrt{2}.

$$6+15\sqrt{2}+18$$

Add 6 and 18 to get 24.

$$24+15\sqrt{2}$$

Factor

$$3 {(5 \sqrt{2} + 8)} = 45.213203436$$