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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2

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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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What is the value of integer n if \((\sqrt{\frac{16}{10^n}})^2=0.04^2\)

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.
[Reveal] Spoiler: OA

Last edited by Divyadisha on 09 Aug 2016, 04:53, edited 4 times in total.
Edited the question and the OA.

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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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New post 12 Jul 2016, 01:09
I am getting n=4 , I don't know where I am going wrong

EBITDA wrote:
What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.

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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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New post 12 Jul 2016, 01:15
EBITDA wrote:
What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.



Given (√(16/(10^n)))^2 = 0.04^2.

Now on LHS we can get rid of square root due to the square.

Then it becomes

=> (16/(10^n) = 0.0016

16 * 0.0001 = 0.0016

Cancelling 16 on both sides we get the below.

Now it changes to 1/\(10^n\) = 0.0001

Cross multiplying

1/ 0.0001 = \(10^n\)
\(10^4\) = \(10^n\).

So n = 4.

Last edited by msk0657 on 12 Jul 2016, 03:41, edited 2 times in total.

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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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New post 12 Jul 2016, 02:53
msk0657 wrote:
EBITDA wrote:
What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.



Given (√(16/(10^n)))^2 = 0.04^2.

Now on LHS we can get rid of square root due to the square.

Then it becomes

=> (16/(10^n) = 0.0016

16 * 0.001 = 0.0016

Cancelling 16 on both sides we get the below.

Now it changes to 1/\(10^n\) = 0.001

Cross multiplying

1/ 0.001 = \(10^n\)
\(10^3\) = \(10^n\).

So n = 3.

Option D is the correct option.


Hi msk0657,

The part of your answer that I have marked in red is wrong.

It should be 16 * 0.0001 = 0.0016

Nonetheless, here is my approach.

First, I eliminate the square root and the square.

16 / (10^n) = (4 / 100)^2 ---> 16 / (10^n) = 16 / 10,000

Then, I eliminate the 16.

1/ (10^n) = 1 / 10,000

This equals:

10,000 = 10^n

Therefore, n = 4.

Could someone please explain where am I making an error?

Thank you so much.

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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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New post 12 Jul 2016, 03:32

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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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New post 12 Jul 2016, 03:38
EBITDA wrote:
What is the value of integer n if \((\sqrt{\frac{16}{10^n}})^2=0.04^2\)

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.



Hi there,

That is typing mistake...I missed it... it has to be 16 * 0.0001 = 0.0016 ( 0.04 * 0.04 )

It looks like you posted wrong option too.. Bunuel edited the question and I edited my previous solution and n will be 4.

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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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New post 12 Jul 2016, 03:42
msk0657 wrote:
EBITDA wrote:
What is the value of integer n if \((\sqrt{\frac{16}{10^n}})^2=0.04^2\)

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.



Hi there,

That is typing mistake...I missed it... it has to be 16 * 0.001 = 0.0016 ( 0.04 * 0.04 )

It looks like you posted wrong option + question too.. Bunuel edited the question and I edited my previous solution and n will be 4.


I was given a wrong official answer. The correct answer is option E, as already stated above.

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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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New post 08 Aug 2016, 13:35
my solution:
1. get rid of the square power on both sides
\(\frac{16}{10^n}=0.0016\)

2. put the unknown variable on left side

\(10^n= \frac{16}{0.0016}\) and now \(0.0016 = 16*10^(-4)\) so we get

\(10^n=\frac{16}{16}*10^4\) switch signs to +4 power when placed from denominator to nominator


3. \(10^n=1*10^4\) or n=4

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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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New post 22 Aug 2017, 09:43
What is the value of integer n if (1610n−−−√)2=0.042(1610n)2=0.042

A) 0
B) 1
C) 2
D) 3
E) 4

Answer:
cancel the squares oon both sides,
then remove the root on 16/10^n
then it is equal 4/10^2/n=.04
then this equal to 100=10^n/2
then n =4

answer =E=4

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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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New post 22 Aug 2017, 12:06
EBITDA wrote:
What is the value of integer n if \((\sqrt{\frac{16}{10^n}})^2=0.04^2\)

A) 0
B) 1
C) 2
D) 3
E) 4

Please explain in detail your answer.

Thank you.

\((\sqrt{\frac{16}{10^n}})^2=0.04^2\)

\({\frac{16}{10^n}}=0.0016\)

\({\frac{16}{10^n}} = 16 * 10^{-4}\)

\({\frac{16}{10^n}} = {\frac{16}{10^4}}\)

\(n = 4\)

Answer E

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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 [#permalink]

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New post 24 Aug 2017, 15:11
EBITDA wrote:
What is the value of integer n if \((\sqrt{\frac{16}{10^n}})^2=0.04^2\)

A) 0
B) 1
C) 2
D) 3
E) 4


We can simplify the given equation and we have:

16/10^n = (4/100)^2

16/10^n = 16/100^2

Since the numerators are equal, the denominators should also be equal:

10^n = 100^2

10^n = (10^2)^2

10^n = 10^4

n = 4

Answer: E
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Re: What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2   [#permalink] 24 Aug 2017, 15:11
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