Problem with notation for square roots

[Harry_the_cat]

Are these two expressions the same? That is, can the square root symbol always be interpreted as raising to an exponent of \(\displaystyle \frac{1}{2}\).

1. \(\displaystyle \sqrt{(-1)^2}\)

2. \(\displaystyle ((-1)^2)^{\frac{1}{2}}\)

It would appear to me that

\(\displaystyle \sqrt{(-1)^2}=\sqrt{1}=1\)

whereas

\(\displaystyle ((-1)^2)^{\frac{1}{2}}= (-1)^{(2*\frac{1}{2})}=(-1)^1=-1\).

What's going on here? The two different notations imply a different order of operation, so they are not the same. Thoughts?

 

[Saumyojit]

Complex no

why does -3^2 translate to -9 . I thought -3^2 meant (-3)^2 which gives me 9 . Is there any connection of Bedmas with the evaluation of this expression. First, BEDMAS is a simplifying acronym designed to help beginning students. Second, the minus sign means has at least three different...

www.freemathhelp.com

u will find some relevance

 

[Harry_the_cat]

Thanks for the link, but they are not really addressing the notation issue of sqrt symbol vs raising to power of 1/2. And I'm not concerned with complex numbers.

 

[Saumyojit]

Thanks for the link, but they are not really addressing the notation issue of sqrt symbol vs raising to power of 1/2. And I'm not concerned with complex numbers.

see the '27' eg there and post no 31 and please come to conversation I am still waiting

 

[Harry_the_cat]

see the '27' eg there and post no 31 and please come to conversation I am still waiting

I just want to see what response I get here. That conversation is a bit all over the place for me.

 

[Saumyojit]

I just want to see what response I get here. That conversation is a bit all over the place for me.

ok please come to conversation . I feel dizzy now

 

[Harry_the_cat]

?

 

[Saumyojit]

I still didn't understand of your explanation of taking the square root by just cancellation of squares part .
Please come to Conversation.