Harry_the_cat
Elite Member
- Joined
- Mar 16, 2016
- Messages
- 3,697
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?
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?