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# Rationalize

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Simplify and rationalize the denominator: 1/(1 + 1/(sqrt(3) + 2)).

Oct 11, 2022

#1
+1015
+1

$$1\over1+{1\over\sqrt{3}}+2$$

Multiply top and bottom by root3 and combine 1 + 2.

$$\sqrt{3}\over3\sqrt{3}+1$$

Multiply top and bottom by $$3\sqrt{3}-1$$

$$\sqrt{3}(3\sqrt{3}-1)\over(3\sqrt{3}+1)(3\sqrt{3}-1)$$

$$9 - \sqrt{3}\over26$$

Oct 11, 2022
#2
0

That answer is wrong.

Guest Oct 12, 2022