Understanding the Complexities of Square Roots in Equations

  • Thread starter madness
  • Start date
In summary, the conversation discusses a paradox involving the square root of a negative number. The person is unsure about the validity of using the formula sqrt(a/b)=srt(a)/sqrt(b) and seeks clarification. It is explained that this formula is not always true because every number except 0 has two square roots with opposite sign. A helpful resource is also mentioned for further understanding.
  • #1
madness
815
70
I have come up with a simple "paradox" (obviously I am doing something wrong). Sorry I can't use latex:

(-1)/1=1/(-1), take square root of both sides, so sqrt((-1)/1)=sqrt(1/(-1))
use sqrt(a/b)=srt(a)/sqrt(b) *, so i/1=1/i, implies i squared =1.

I think the problem is the part marked *, but I'm not sure in what circumstances this is valid. Can anybody help?
 
Mathematics news on Phys.org
  • #2
The problem is that every number except 0 actually has two square roots with opposite sign. You can arbitrarily choose one for each number, but then the formula sqrt(a/b)=srt(a)/sqrt(b) is not always true (as you demonstrated).

See also http://en.wikipedia.org/wiki/Square_root#Notes"
 
Last edited by a moderator:
  • #3
Ok that helps a lot. The example on wikipedia was pretty much exactly the one I posted. Thanks.
 

FAQ: Understanding the Complexities of Square Roots in Equations

What is the purpose of having rules in scientific research?

Rules in scientific research serve to ensure that experiments and studies are conducted in a safe and ethical manner. They also help to maintain the accuracy and reliability of the results obtained.

How do I know if I am breaking a rule in my research?

You can determine if you are breaking a rule in your research by familiarizing yourself with the relevant guidelines and protocols set by your institution or governing body. It is important to regularly review and follow these rules to avoid any violations.

What are some common rules that are often broken in scientific research?

Some common rules that are often broken in scientific research include plagiarism, fabrication or falsification of data, failure to obtain proper consent from participants, and not following proper safety procedures.

What are the consequences of breaking a rule in scientific research?

The consequences of breaking a rule in scientific research can vary depending on the severity of the violation and the policies of your institution or governing body. They can range from a warning or reprimand to loss of funding, publication, or even legal action.

How can I avoid breaking rules in my scientific research?

To avoid breaking rules in your scientific research, it is important to stay informed and up-to-date on the relevant guidelines and protocols. You should also regularly consult with your supervisor or a research ethics committee for guidance and ensure that all procedures and protocols are followed carefully.

Similar threads

B Principal square root of a complex number, why is it unique?
Replies
13
Views
4K
I Trouble Solving an Equation that has square roots on both sides
Replies
1
Views
1K
B Determine a fractional square root without calculator
Replies
15
Views
1K
B Square root of a negative number in a complex field
2
Replies
45
Views
5K
I Newton-Raphson Method With Complex Numbers
Replies
7
Views
2K
B Simplifying roots of negative numbers
Replies
2
Views
1K
MHB Can Cubic Roots and Square Roots Combine to Equal One?
Replies
5
Views
2K
MHB How to Solve the Radical Equation Using Fifth Root and Square Root?
Replies
3
Views
1K
B Resolving index laws for fractional exponents
Replies
2
Views
1K
I Is it valid to express a complex number as a vector?
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top