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# 0.00001^(1/2) =

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Math Expert
Joined: 02 Sep 2009
Posts: 49273

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18 Jul 2018, 00:40
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Difficulty:

35% (medium)

Question Stats:

55% (01:01) correct 45% (01:13) wrong based on 31 sessions

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$$\sqrt{0.00001}$$ =

A) $$\frac{\sqrt{10}}{100}$$

B) $$\frac{1}{100}$$

C) $$\frac{\sqrt{10}}{1000}$$

D) $$\frac{1}{1000}$$

E) $$\frac{\sqrt{10}}{10000}$$

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Joined: 22 Feb 2018
Posts: 320

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18 Jul 2018, 01:02
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Bunuel wrote:
$$\sqrt{0.00001}$$ =

A) $$\frac{\sqrt{10}}{100}$$

B) $$\frac{1}{100}$$

C) $$\frac{\sqrt{10}}{1000}$$

D) $$\frac{1}{1000}$$

E) $$\frac{\sqrt{10}}{10000}$$

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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18 Jul 2018, 01:12
Bunuel wrote:
$$\sqrt{0.00001}$$ =

A) $$\frac{\sqrt{10}}{100}$$

B) $$\frac{1}{100}$$

C) $$\frac{\sqrt{10}}{1000}$$

D) $$\frac{1}{1000}$$

E) $$\frac{\sqrt{10}}{10000}$$

$$\sqrt{0.00001}........................\sqrt{\frac{1}{100000}}=\frac{1}{100}*\sqrt{\frac{1}{10}}.........................\frac{\sqrt{10}}{1000}$$

C
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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18 Jul 2018, 04:59
Approach and Working:

$$\sqrt{(0.00001)}= \sqrt{(1/10^5)}= \sqrt{(10/10^6)}= \frac{\sqrt{10}}{ 10^3}= \frac{\sqrt{10}}{ 1000}$$

Hence, the correct answer is option C.

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