Solve 4(6sqrt{3}+72)(6sqrt{3}-sqrt{2})=

$$4 ( 6 \sqrt { 3 } + 72 ) ( 6 \sqrt { 3 } - \sqrt { 2 } ) =$$

Evaluate

$$1728\sqrt{3}+432-24\sqrt{6}-288\sqrt{2}\approx 2958.902535689$$

Solution Steps

Use the distributive property to multiply 4 by 6\sqrt{3}+72.

$$\left(24\sqrt{3}+288\right)\left(6\sqrt{3}-\sqrt{2}\right)$$

Apply the distributive property by multiplying each term of 24\sqrt{3}+288 by each term of 6\sqrt{3}-\sqrt{2}.

$$144\left(\sqrt{3}\right)^{2}-24\sqrt{3}\sqrt{2}+1728\sqrt{3}-288\sqrt{2}$$

The square of \sqrt{3} is 3.

$$144\times 3-24\sqrt{3}\sqrt{2}+1728\sqrt{3}-288\sqrt{2}$$

Multiply 144 and 3 to get 432.

$$432-24\sqrt{3}\sqrt{2}+1728\sqrt{3}-288\sqrt{2}$$

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

$$432-24\sqrt{6}+1728\sqrt{3}-288\sqrt{2}$$

Factor

$$24 {(72 \sqrt{3} + 18 - \sqrt{6} - 12 \sqrt{2})} = 2958.902535689$$