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# help!

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Rationalize the denominator of: $$\frac{1}{\sqrt{2}+\sqrt{8}+\sqrt{32}}$$. The answer can be written as $$\frac{\sqrt{A}}{B}$$, where $$A$$ and $$B$$ are integers. Find the minimum possible value of $$A+B$$.

Feb 22, 2023

#1
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The denominator of 1/(sqrt(2) + sqrt(8) + sqrt(32)) can be rationalized by multiplying both numerator and denominator by -sqrt(2) + sqrt(8) + sqrt(32). This gives us (-sqrt(2) + sqrt(8) + sqrt(32))/(-2 + 8 + 32) = sqrt(2)/19.

The final answer is 2 + 19 = 21.

Feb 22, 2023
#2
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$${1 \over \sqrt{2} + \sqrt{8} + \sqrt{32} }$$

$${1 \over \sqrt{2} + 2\sqrt{2} + 4\sqrt{2} }$$

$${1 \over 7\sqrt{2} }$$

$${1 \over 7\sqrt 2} \times { \sqrt{2} \over \sqrt {2}}$$

$${\sqrt 2 \over 14}$$

$$2 + 14 = \color{brown}\boxed{16}$$

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Feb 22, 2023
#3
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