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

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

Evaluate

$$72\sqrt{2}+132\approx 233.823376491$$

Solution Steps

Combine \sqrt{3} and \sqrt{3} to get 2\sqrt{3}.

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

Expand \left(2\sqrt{3}\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

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

Multiply 4 and 3 to get 12.

$$12\left(3+\sqrt{2}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+\sqrt{2}\right)^{2}.

$$12\left(9+6\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

The square of \sqrt{2} is 2.

$$12\left(9+6\sqrt{2}+2\right)$$

Add 9 and 2 to get 11.

$$12\left(11+6\sqrt{2}\right)$$

Use the distributive property to multiply 12 by 11+6\sqrt{2}.

$$132+72\sqrt{2}$$

Expand

$$72 \sqrt{2} + 132 = 233.823376491$$

Solution Steps

Combine \sqrt{3} and \sqrt{3} to get 2\sqrt{3}.

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

Expand \left(2\sqrt{3}\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

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

Multiply 4 and 3 to get 12.

$$12\left(3+\sqrt{2}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+\sqrt{2}\right)^{2}.

$$12\left(9+6\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

The square of \sqrt{2} is 2.

$$12\left(9+6\sqrt{2}+2\right)$$

Add 9 and 2 to get 11.

$$12\left(11+6\sqrt{2}\right)$$

Use the distributive property to multiply 12 by 11+6\sqrt{2}.

$$132+72\sqrt{2}$$