[doghouseriley]

I was doing a question involving a line meeting an irrational function. When solving the equation to find the common point, two solutions for x came out of the working, but one had to be discarded. When sketching the graphs it was obvious which solution to discard, but then the next problem wanted you to work out which solution to discard without reference to a sketch or graph.

It looked like a simple thing to do. You take each solution, substitute it in the left hand side/right hand side of original equation and if the don't match that is the one to discard. However, when I did this I had the following situation:

Left hand side = -2
Right hand side = sqrt (4)..... The book said this is the one to discard! But i thought sqrt (4) would mean it could be +2 or -2... But somewhere in the past I remember hearing that the sqr root symbol actually implies 'take the positive' root. Is this correct?

[Hearty_Beast]

I'm pretty sure it's both + and - , unless you use modulus.

[pbsjohnz]

Positive square root is for when something can only be positive. eg the length of something cannot be negative, so you take only the positive square root.

[Bobifier]

Traditionally we use the square root symbol to refer to the positive square root whilst bearing in mind that there also are other options. If you find yourself in a situation in which the symbol is ambiguous enough that you are not sure people will know what you mean it is best to clarify verbally. If you find yourself in a situation where only one of the available square roots makes sense as a solution then you should use that one.

[Arbolus]

Normally when using a square root sign we assume that it's talking about the positive root. If it could be either then put a +/- in front of it.

[f1mad]

Generally the square root of a number is taken to be the positive square root.

The square root of an equation i.e x^2=4, implies the positive and negative square root: e.g. x= +-sqrt4.

[Jake22]

The square root sign is normally used to denote the application of the function 'take the square root of'

Therefore, it should only have one value i.e. the positive square root. In situations where you want to consider the possibility of both square roots you should write .

Indeed, this tallies with the excerpt of whatever it is you have quoted.

[doghouseriley]

So in my original question, where I had to exclude a solution without looking at anything else other than the thing below, this seems to back up what you say -root symbol means 'take positive root.' (there was nothing about x representing a real line or anything, it was purely about finding the point where a line met an irrational function.)

The two situations were.

Test for solution 1

LHS = 2, RHS = Sqr (4) allow this solution as LHS = RHS

Test for solution 2

LHS = -2, RHs = sqr (4) discount this solution as the LHS does not equal RHS.

The only way i can see this to be true is if you take sqrt symbol to mean 'take' positive root.

[Manitude]

Depending on the situation (but not always!) you may ignore either the positive or negative root. For example with certain physical quantities or where the question states that the solution is positive.

[doghouseriley]

Something has just dawned on me! All this came about from doing a section titled "Graphs of irrational functions". For instance, first thing was to plot

Graph

As a matter of interest what would you plot? A graph that was single valued or multivalued. E.g. for each positive value of would you have 1 or 2 values for ?