Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Principal Square Root Definition

College Algebra
Section R.2

Please explain, in your own words, the definition of the principal square root.

Sullivan stated the following definition on page 23.

If a is a nonnegative real number, the nonnegative number b such that b^(2) = a
is the principal square root of a, and is denoted by b = sqrt{ a }.

The definition is not too clear.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Principal Square Root Definition

Most numbers (ie unless zero) have two square roots. The principal root is the positive one.

You posted a whole string of posts on the same subject. It has been hard for me to check if I've replied to them all.  It would be easier if you either (i) waited for the first reply and then asked the next question as a further reply to that; or (ii) put all you questions in one post, numbering them so I can be sure I've got them all covered.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Principal Square Root Definition

Bob,

You are right. I apologize for posting so many questions all at once. I will do as you say. I will post one problem at a time and wait for a reply to continue our discussion. Sometimes, I get overly excited when it comes to math.

So, when we take the square root there are always two answers:

A. Positive

B. Negative

The P.S.R. represents the positive answer.

P.S.R = PRINCIPAL SQUARE ROOT

so, sqrt{81} = -9 and 9.

The P.S.R. answer is 9, that is, positive 9.