The square of a numberis always positive. True or false. If false correct & please give reference books if any

Answer 1

No, because zero is a number, and 0² = 0, which isn't positive. Also the squares of imaginary numbers can give you negative numbers (though if you haven't learned about imaginary numbers yet, skip that notion for now and just go with the first example I gave.)

Answer 2

Yes and no. The square of a real number will be positive (excpt for the case of zero because zero is neither positive of negative).

The square of an imaginary number could be negative for example in the most simple case i^2 = -1 where i=sqrt(-1).

Complex numbers dont usually appear until you start with some more heavy maths so depending on your level of understanding i wouldnt worry too much about them. For further information just ggoogle 'Complex Numbers' and I'm sure you will find alot of info

Answer 3

Somtimes square of number is negative in case of imaginary numbers, where you have Square root of (-1) denoted as i.
i is an imaginary number whose square is negative.
i x i = -1
This you will get in any book on complex number. There are good problems based on this concept.

So answer to your question depends on your syllabus. If you are not stuyding advance mathematics you can simply say "True".
Else you have to give the above justification with a "False" answer.

Answer 4

False. The square of 0 is 0, which, by definition, is not a positive number (a number is positive if and only if it is greater than 0; 0 cannot be greater than itself).

Answer 5

Yes the square of any number is always positive. This is valid for all real numbers. But there is a set of complex numbers, in which the square of a number may be negative.
This is because, in real nos, square root of negative nos is not defined and there you will find all squares positive.

Answer 6

True because a negative multiplied by a negative is positive

Answer 7

The square of ANY number is only positive.... i'll prove it.

if the number is positive.....(be it x)...
then its square is (+x) * (+x)....= (plus * plus)(x * x)
+ multiplied by + is +......therefore the square is +x^2

if the number is negative..... (be it -y)
then its square is (-y)(-y) = (minus * minus)(y *y)
minus * minus = plus.
therefore, ans:- +y^2

so the square is always +ve...
suppose the square is negative... it is an imaginary no.(complex no.)

Answer 8

its true..coz negative into negative makes positive.