How do you simplify (6+ square root 3)(6-square root 3)?

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How do you simplify (6+ square root 3)(6-square root 3)?

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Answer 1 · 2015-07-20T02:27:06

$(6 + \sqrt{3}) \cdot (6 - \sqrt{3}) = 6^{2} - {(\sqrt{3})}^{2} = 36 - 3 = 33$ $(6+sqrt(3))*(6-sqrt(3))=6^2-(sqrt(3))^2=36-3=33$

Explanation:

General property this problem is based upon is
$(a + b) \cdot (a - b) = a^{2} - b^{2}$ $(a+b)*(a-b)=a^2-b^2$

Indeed, if we open the parenthesis in the original expression, we get:
$(a + b) \cdot (a - b) = a \cdot a + b \cdot a - a \cdot b - b \cdot b = a^{2} - b^{2}$ $(a+b)*(a-b)=a*a+b*a-a*b-b*b=a^2-b^2$

Using the above property for $a = 6$ $a=6$ and $b = \sqrt{3}$ $b=sqrt(3)$ , we obtain
$(6 + \sqrt{3}) \cdot (6 - \sqrt{3}) = 6^{2} - {(\sqrt{3})}^{2} = 36 - 3 = 33$ $(6+sqrt(3))*(6-sqrt(3))=6^2-(sqrt(3))^2=36-3=33$

So, $33$ $33$ is the final answer.

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How do you simplify (6+ square root 3)(6-square root 3)?

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