Math Is Fun Forum

PatternMan

Member

Registered: 2014-03-08

Posts: 199

Please explain

Isn't the the square root of a number eg 25. 5 or -5? When I solved quadratic equations I would use this method. In desmos a graphing program the square root is only outputting the positive square root regardless of whether I make it a function or not. So the function has only one output. But why does it only take the positive root and how do I know when this applies?

f(x) = sqrt(x)
f(9) = 3?
y = sqrt(9)

https://s3.amazonaws.com/grapher/exports/9gjyy99zft.png

Last edited by PatternMan (2014-08-11 23:18:13)

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"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Please explain

hi PatternMan,

Yes, you're right.  But programmers of graph plotting software (like calculators) want a single valued result so they leave out the negative answer.  They same happens with inverse trig functions

eg. arcsin(0.5) = 30, or 150, or 390, or 510, or ....... but a calculator will only tell you the first value.

The student is expected to know this and to be able to pick the correct answer for a given problem.

eg.  I'm thinking of a number, over 10.  When I subtract it from 10 and square the result, I get 9.  What is the number ?

But the wording of the question forces me to pick 13 as the only solution.

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

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Please explain

A function can have only 1 output.

In f(x)  = √x, it will only give the positive root.

PatternMan

Member

Registered: 2014-03-08

Posts: 199

Re: Please explain

A function can have only 1 output.

In f(x)  = √x, it will only give the positive root.

Why don't they take the negative root instead? I read they take the absolute value. Is it just convention?

Last edited by PatternMan (2014-08-12 00:18:25)

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"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Please explain

Is it just convention?

Yes.

√  is taken to mean the positive root.

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