Question

Is there a real number ______ whose square is -1? b. Does there exist _____ such that x 2 = −1?

Answer 1

Answer:

no , negative square roots do not exist.

Step-by-step explanation:

Negative numbers don't have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers.

thus $x^{2}$= -1 does not exist

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Answer 2

Given  :  Is there a real number  whose square is -1

Does there exist  real number x  such that x² = −1

To Find :  yes or No

Solution:

Square of real numbers are non negative numbers

Hence there is no real number whose square is - 1

-1 is square of iota    

i² = - 1

and i is imaginary number

Therefor there does not exist any real numbers  whose square is -1

x² = - 1

so there does not exist  any real number x , satisfying this

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