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If n denotes a number to the left of 0 on the number line

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Re: If n denotes a number to the left of 0 on the number line [#permalink]

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New post 09 Jan 2018, 04:59
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dave13 wrote:
AKProdigy87 wrote:
The answer is A.

We are given two pieces of information:

1) \(n^2 -\frac{1}{10}\)

To determine the conditions on the reciprocal of n:

\(\frac{1}{n}

for example if [m]\sqrt{x}\) = 4 then we need to squae both sides of equation

so \(\sqrt{(x)}\) = \((4)^2\)

---> x= 16

now when it comes to the solution above from this equation \(n^2 < \frac{1}{100}\) we get this \(|n| < \frac{1}{10}\) - why ? should not we square both sides as I did in my example ? :?

Why are we applying this formula \(\sqrt{x^2}\) = \(|x|\) if this doesnt look like \(n^2 < \frac{1}{100}\) ? <-- (here we dont have radical sign) why 100 in denominator is reduced by 10 ? shouldn't 100 be multiplied by itself as in my example ? in my example the number 4 turns into 16 and here it get reduced...so I am confused

Also ss there a difference between \(\sqrt{x^2}\) and \(\sqrt{x}\) ?

many thanks ! :)

perhaps you friends can help :? :-) chetan2u , niks18


Always remember the rule -
\(\sqrt{x}=5\) wll have only one solution as x=25
that is \(\sqrt{25}\) will always be 5 because square root cannot be negative

But \(x^2=25\) means x can be 5 or -5
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If n denotes a number to the left of 0 on the number line [#permalink]

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New post 09 Jan 2018, 07:09
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hi dave13

Quote:
for example if \(\sqrt{x}\) = 4 then we need to squae both sides of equation

so \(\sqrt{(x)}\) = \((4)^2\)

---> x= 16

now when it comes to the solution above from this equation \(n^2 < \frac{1}{100}\) we get this \(|n| < \frac{1}{10}\) - why ? should not we square both sides as I did in my example ? :?


Note: \(\sqrt{n^2}=|n|\), because here \(n\) is a variable and you don't know the value. for eg. \((-2)^2=4\) & \((2)^2=4\)

so if we say \(n^2=4\), then on taking square root of both sides we will have \(n=|2|=2\) or \(-2\)

Hence here for \(n^2 < \frac{1}{100}\) we get \(|n| < \frac{1}{10}\) on taking square root of \(n^2\), because \(n\) is a variable here

Quote:
Why are we applying this formula \(\sqrt{x^2}\) = \(|x|\) if this doesnt look like \(n^2 < \frac{1}{100}\) ? <-- (here we dont have radical sign) why 100 in denominator is reduced by 10 ? shouldn't 100 be multiplied by itself as in my example ? in my example the number 4 turns into 16 and here it get reduced...so I am confused


we are taking square root here and not squaring. as we have \(n^2\) so by taking square root we will get to \(|n|\); \(100=10^2\) and \(\sqrt{10^2}=10\)

Quote:
Also ss there a difference between \(\sqrt{x^2}\) and \(\sqrt{x}\) ?

many thanks ! :)


There is a lot of difference between \(\sqrt{x^2}\) and \(\sqrt{x}\)

let's assume \(x=2\), then \(x^2=4\) and \(\sqrt{4}\) is different from \(\sqrt{2}\)

Kudos [?]: 379 [1], given: 42

If n denotes a number to the left of 0 on the number line   [#permalink] 09 Jan 2018, 07:09

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