Kathy S.

asked • 08/20/15

Why is the square root of 64 only positive 8, not negative 8?

If the square of -8 is also 64, why isn't the square root of 64 also -8?

3 Answers By Expert Tutors

By:

Dominic S. answered • 08/20/15

Tutor
5.0 (240)

Math and Physics Tutor

Kathy S.

Thank you! I appreciate all the answers on this question very much but I thought yours made the most sense to me. Thanks again! :-)
Report

08/21/15

Shradha S. answered • 08/21/15

Tutor
4 (1)

Experienced Maths Teacher with Master's Degree in Mathematics

David W. answered • 08/20/15

Tutor
4.7 (90)

Experienced Prof

Michael W.

A square root of a number could be positive or negative.  However, my understanding is that the square root symbol (√) refers to the principal square root.  The positive one.  Right? 
 
That's why, if we want to talk about both the positive and the negative square roots, we put a ± in front of the √...so I'm with Dominic on this one.  "The" square root of 64, written √64, is 8, by convention.
Report

08/21/15

David W.

Wow, some research is warrented.
 
      √64 = ±8
 
So, if you write ±√(b2-4ac), the surd could simply represent a clarification, like an extra set of parenthesis in (±(±8)).  Does it?
 
Now, PLZ put a digit (say 3 or 4) above the horizontal line and continue the discussion (and PLZ continue to use the words "convention" and "clarification").
 
 
Report

08/21/15

Michael W.

David, according to the very article that you cited on Wikipedia, √64 is not equal to ±8.  It's equal to 8.  The radical sign means "principal square root," and that's the positive version.
 
Kathy asked what the square root of 64 was, so either it's asking for the principal square root (which is implied), or it's asking for the square roots of 64.  I guess it could have been asking for either one, but I was just leaning towards the first version, which seemed more intuitive.
 
 
Report

08/21/15

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.