Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Principal Square Root

College Algebra
Section R.2

Michael Sullivan introduces the idea of square roots on page 24.

According to Sullivan:

sqrt{ a^2 } = | a |, where "a" is any real number.

Sample:

sqrt{ x^2 } = | x |.

Why is the answer the absolute value of x and not simple x?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Principal Square Root

Because x could be negative and he is trying to define a unique positive root.

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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

Are you saying that the sqrt{ x^(2) } = -x or x?
To assure a positive x, we place the variable x inside absolute value bars.

Yes?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Principal Square Root

Yes.

---

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

Thank you, Bob.