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

Question

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.

vivekkumar987 · Answer

I am getting n=4 , I don't know where I am going wrong

msk0657 · Answer

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.

EBITDA · Answer

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.

Bunuel · Answer

The OA is wrong. The correct answer is 4 (E)

msk0657 · Answer

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.

EBITDA · Answer

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

kzivrev · Answer

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

abhishekdadarwal2009 · Answer

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

generis · Answer

(\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

ScottTargetTestPrep · Answer

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

Amritaachopra17 · Answer

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.

Krunaal · Answer

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

Amritaachopra17 · Answer

this helps, thank you

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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

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