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Rewrite equation as \(\sqrt{1*10^{-5}}\), where 1 will come out as 1 and \(10^{-5}\) is \(10^{-4}*10^{-1}\) when divided by 2 ( square root) will be \(10^{-2}*10^{-1/2}\)
\(1/{100*\sqrt{10}}\)
to get rid of square root in denominator we multiply both sides with \(\sqrt{10}\) and get \(\sqrt{10}/{100*10}\). Answer C
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the answer is attached. this question was tricky because the exponents and roots component. thanks for your responses, you helped me to better understand this problem.
Let's take a closer look at √100,000 √100,000 = √(10,000 x 10) = (√10,000)(√10)[applied rule #2] = 100(√10)
So, 1/(√100,000) = 1/100√10 Check the answer choices...not there. Looks like we need to "fix" (rationalize) the denominator (for more on this, check the video below) Multiply top and bottom by √10 to get: (√10)(1)/(√10)(100√10) Simplify: (√10)/1000 Answer:
OA: C \(\sqrt{0.00001}\) = \(\sqrt{10^{-5}}=10^{-2}*10^{-\frac{{1}}{{2}}}= \frac{1}{{100\sqrt{10}}}\) Multiplying numerator and denominator by \(\sqrt{10}\) \(\frac{{1}}{{100\sqrt{10}}}\)\(*\)\(\frac{{\sqrt[]{10}}}{{\sqrt[]{10}}}\) \(=\frac{{\sqrt[]{10}}}{1000}\)
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