Math problem that creates some confusion

[Chambokl]

This is the Fibonnaci sequence... It is an interesting sequence.... If you take the ratio of 2 consecutive number it is really close the the Golden Number (or golden ratio)

1, 1, 2, 3, 5, 8, 13, 21, 34, ....

[Chambokl]

Sorry, but you are wrong on that one. It is a simplification to say that the square root of 9 is 3, but it is precise to say either "a square root of 9 is 3" or "the square roots of 9 are +3 and -3".

A square root is that number which, when multiplied by itself, gives the target number. So, it is either the positive or the negative.

Trust me Shark.... the square root of a number is always and only positive....

That is why in example 3, you have to use the plus and minus sign in front of the square root!!

Maths.png

[sharkshooter]

Trust me Shark.... the square root of a number is always and only positive....

Can we move on now?

[mpare]

I don't believe that we have wrestled this issue to the ground, yet.

Can we move on now?

[Kilroy]

Still on page 1

[mpare]

My understanding has been that one asks for the square root of a non-negative real number one is implicitly asking for the principal square root of that number, which is itself a postive number. However, postive real numbers also have negative square roots. If one wishes to express that mathematically, then a minus sign would be placed before the square root symbol. Finally, if one wanted both the positive and the negative roots, then one would place the + and - signs before the symbol for square root. Is this not correct?

[Chambokl]

My understanding has been that one asks for the square root of a non-negative real number one is implicitly asking for the principal square root of that number, which is itself a postive number. However, postive real numbers also have negative square roots. If one wishes to express that mathematically, then a minus sign would be placed before the square root symbol. Finally, if one wanted both the positive and the negative roots, then one would place the + and - signs before the symbol for square root. Is this not correct?

Yes Mike.... absolutely correct. That is why in the 3rd example.... When using the quadratic formula you have a + and a - in front since the square root will give you the positive answer only!!

PS: You should be golfing and not worry about square roots....

[mpare]

Jean-Guy, don't worry. I have been playing golf everyday day save one since I arrived here on the 29th. I'll hit a few for you.

...

PS: You should be golfing and not worry about square roots....

[Chambokl]

Jean-Guy, don't worry. I have been playing golf everyday day save one since I arrived here on the 29th. I'll hit a few for you.

Awesome... and make sure they are straight... Oh sorry, you always hit straight (from what I remember)... Enjoy yourself...

Since you like the Fibonnaci sequence here is another one.... Take any 2 numbers and do your own sequence following the Fibonnaci idea.

Example..... I will take 71 and 12

71, 12, 83, 95, 178, 273, 451, 724, 1175, 1899, ....

Now divide 2 consecutive numbers 1899/1175 = 1.61617 which is close to the Golden Number (1.618)

You could spend a couple of nights reading about the beauty of the Golden Number....

[sharkshooter]

...Now divide 2 consecutive numbers 1899/1175 = 1.61617 which is close to the Golden Number (1.618)

....

And the higher up you go, the closer to the Golden Number, which is, of course, an irrational number.