SOLUTION: why square root of -2 is not a real number and what we have to see a number is real or not

Question 884962: why square root of -2 is not a real number and what we have to see a number is real or not
Found 2 solutions by josgarithmetic, dkppathak:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
sqrt(-2) is imaginary. REAL numbers have REAL solutions for for . n does not need to be a perfect square. n just needs to be positive or equal to zero.

You know can be solved to find x=2 or x=-2. How? , .

You know can be solved to find x=5 or x=-5.

Try .

; What is that?

Square root of a positive number we can make sense. Square root of a negative number is different. One way to deal with this was to invent a different kind of number. uses the imaginary number, i, according to this shown equation. Now with that simple-looking equation, the square root can be found as .

The number, i, is often used as the imaginary unit to help in writing imaginary numbers.
(I have included the 0 in a couple of the equations only to help with rendering. Usually, that addition or subtraction of zero is unnecessary).

Square Root of -2
---------------------

which is an imaginary number.
Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
why square root of -2 is not a real number and what we have to see a number is real or not
solution
square root of negative number not defined as we know square root of 4 is +2 and -2 when we take square root of negative it self . it can not defined
for this purpose sqrt of (-2) can be written as squrt 2 x sqrt (-1)
sqrt (-1) is term as imaginary number i (iota)
therefor sqrt (-2) = squrt 2 x sqrt (-1) = sqrt 2 xi which is again Imaginary number
so real number ( rational or irrational ) or which can be represent on number line is known as real number or which is sqrt with positive number is real
number which can not be represent on number line is Imaginary number or sqrt of negative number is Imaginary
combination of real and Imaginary is called complex number represent as Z
Z=X +iy where X is real and Y is imaginary
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