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 \(\sqrt{2}\)