[R Federer]

I think this should help the debate

http://www.mathpath.org/concepts/pri...quare.root.htm


Try this...

What has gone wrong here:

[shekhar]

Originally Posted by Vengeance

Those which can not be expressed as roots of a polynomial equation with integer cofficients. For example, pi is a transcendental number, while root(2) is not as x^2-2=0
All transcendental are irrationals, converse need not be true.

please explain a bit more....

[21563-S]

Originally Posted by shekhar

please explain a bit more....

You got the defintion, now look for details :-)

http://mathworld.wolfram.com/TranscendentalNumber.html

http://sprott.physics.wisc.edu/pickover/trans.html

[shekhar]

Originally Posted by R Federer

I think this should help the debate

http://www.mathpath.org/concepts/pri...quare.root.htm


Try this...

What has gone wrong here:

in the 3rd step, you are dividing & multipying by 'square root of a -ve no. " which is undefined.

[anupam will return]

Why the square root of a positive real number is taken as positive




We consider here only real numbers. The square root of a positive real number x is a number r satisfying r2 = x. But there is a problem. If r2 = x then (-r)2 = x as well. So the square root of a positive real number has two values, differing only in sign. This is exemplified by the formula for the root of a quadratic equation, say ax2 + bx + c = 0. The roots are (-b ±√(b2 - 4ac))/2a.
So if b = 0 and a = -1, the root is indeed ±√c. The positive square root of a positive real number is called a principal square root. In common usage, the square root of a positive real number is taken as the principal square root. This is why in school, the square root of, say, 4 is taken as +2.
The reason for taking the principal square root as the value of the square root of a positive real number is the following. For the function f(x) = x2, the inverse map, call it g, is g(x) = ±√x. This means g maps x to two values. Then g is not a function. We can make g a function by ensuring that it maps x to a unique value. This can be achieved by assuming a convention where the value of g at x is either always the principal square root of x or always the negative of the principal square root of x. The world of mathematics has adopted the former. Thus g, the square-root map, becomes a function for postive real number x. Now, an inverse map g of f must satisfy the following property: g(f(x))= f(g(x))= 1. With f(x) = x2 and g(x) = √x, this gives √(x2) = x. That is, for positive real number N, we shall mean by the square root of N, the positive square root of N.

[R Federer]

Originally Posted by shekhar

in the 3rd step, you are dividing & multipying by 'square root of a -ve no. " which is undefined.

Hmmm...you mean division and multiplication with complex numbers is undefined?

The funda is closely related to what Anupam asked with square root thing.

[anupam will return]

Originally Posted by shekhar

in the 3rd step, you are dividing & multipying by 'square root of a -ve no. " which is undefined.

I think the error lies in the 2nd step. We all know root(-1) = i,hence,

root(-1) = i (L.H.S)

R.H.S = root (1/-1) = root (1)/i
therefore equating LHS and RHS, i^2 = root(1).
As we know square root of any number is always +ve ( i still want to know how ? )

But by defn.. i^2 = -1.

Hence the fault.

Edit : don't think the above explanation's correct.
root(a)/root(b) = root(a/b), only for real numbers.. hence the fault

[thecky]

Originally Posted by anupam will return

To start with .. one very simple question which was asked once in an IIM-C Interview..

if we take any big number and keep on taking its square root continuously (by continuosly I mean taking the square root of the result of the 1st computation and so on..)
,why do we end up with 1 ?
The same is true for any small number also.. take 0.2 and keep on taking its square root infinitely.. we end up with 1. I want to know the reason for this..

When we take sqrt repeatedly, the power to which any no.(large or small) is
raised tends to 1/infinity i.e. 0. and any no. ^0 =1.

[neo_leo53]

..explaination needed.

.. A man leaves office daily at 7pm.a driver with car comes from his home to pick him from office and bring back home. One day he gets free at 5.30 and instead of waiting for driver he starts walking towards home. In the way he meets the car and returns home on car. He reaches home 20 minutes earlier than usual. In how much time does the man reach home usually?

(A) 1 hr 20 min (B) 1 hr (C) 1 hr 10 min (D) 55 min

[sunilnatraj]

@anupam:

I know I am no stud, but here is my ans why the square root of a number is always +ve:

Consider the foll:
(1^2)=(-1)^2=1
therefore taking sq roots and equating we get: -1=1

to avoid this ambiguity, mathematicians follow a convention that a square root is always +ve.

Note that this only holds for numbers, and not for equations.

therefore,
if x^2=1, then
x=+1 and -1.