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555-605 (Medium)|   Algebra|   Roots|      
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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 Updated on: 09 Aug 2016, 05:53
Originally posted by EBITDA on 12 Jul 2016, 01:53.
Last edited by Divyadisha on 09 Aug 2016, 05:53, edited 4 times in total.
Edited the question and the OA.
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25% (medium)

Question Stats:

77% (01:14) correct 23% (01:26) wrong based on 1743 sessions

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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.
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E
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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 12 Jul 2016, 02:09
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I am getting n=4 , I don't know where I am going wrong

EBITDA
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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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 Updated on: 12 Jul 2016, 04:41
Originally posted by msk0657 on 12 Jul 2016, 02:15.
Last edited by msk0657 on 12 Jul 2016, 04:41, edited 2 times in total.
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EBITDA
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.
Show more


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.
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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 12 Jul 2016, 03:53
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EBITDA
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.
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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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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 12 Jul 2016, 04:32
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EBITDA
What is the value of integer n if \((\sqrt{\frac{16}{10^n}})^2=0.04^n\)

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

Please explain in detail your answer.

Thank you.
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The OA is wrong. The correct answer is 4 (E)
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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 12 Jul 2016, 04:38
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EBITDA
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.
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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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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 12 Jul 2016, 04:42
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EBITDA
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.
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I was given a wrong official answer. The correct answer is option E, as already stated above.
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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 08 Aug 2016, 14:35
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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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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 22 Aug 2017, 10:43
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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 22 Aug 2017, 13:06
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EBITDA
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.
Show more
\((\sqrt{\frac{16}{10^n}})^2=0.04^2\)

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

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

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

\(n = 4\)

Answer E
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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 24 Aug 2017, 16:11
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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
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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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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 05 Feb 2025, 10:20
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Can we not in the first step, take a square root of the whole question? in that case the question will become:

4/√10^n = 0.04. I don't understand why this is wrong.
EBITDA
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.
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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 05 Feb 2025, 12:18
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Can we not in the first step, take a square root of the whole question? in that case the question will become:

4/√10^n = 0.04. I don't understand why this is wrong.
EBITDA
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.
Show more

The square root is inside the parenthesis, so first you solve for the terms inside the parenthesis \((\sqrt{\frac{16}{10^n}})\) = \({\frac{4}{10^{n/2}}}\)

And then you square it again because a square was present outside the parenthesis: \({\frac{16}{10^{n}}}\) = \(0.04^2\) = \({\frac{16}{10^{4}}}\) => n = 4
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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 11 Feb 2025, 20:32
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this helps, thank you
Krunaal
Amritaachopra17
Can we not in the first step, take a square root of the whole question? in that case the question will become:

4/√10^n = 0.04. I don't understand why this is wrong.
EBITDA
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.

The square root is inside the parenthesis, so first you solve for the terms inside the parenthesis \((\sqrt{\frac{16}{10^n}})\) = \({\frac{4}{10^{n/2}}}\)

And then you square it again because a square was present outside the parenthesis: \({\frac{16}{10^{n}}}\) = \(0.04^2\) = \({\frac{16}{10^{4}}}\) => n = 4
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What is the value of integer n if (√(16/(10^n)))^2 = 0.04^2 11 Mar 2026, 06:12
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