True or false?
The square root of any real number is always a real number.
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This is a matter of definition. According to many definitions the square root simply isnt defined for negative numbers and the imaginary numbers are instead just based on i^2=-1 without using the square root. One reason would be the relation to quaternions where this would make the square root multiple valued.
Exactly! The answer is a Imaginary Number.
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You guys be talking crazy. Can't wait to tell my boys you think there's imaginary numbers.
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A very famous mathematician regarded that name as inappropriate. He preferred calling them lateral numbers.
Dude its simple algebra your boys probably already know about them if they are in the 6th grade or higher....
may or may not be.
Real numbers can be negative, and negative numbers have imaginary square roots. For example, − 1 = i
The square root of a negative number is imaginary.
its answer is false because all negative integer also included in real number so square root of a negative number is always complex
The square root of any negative number is imaginary. Notated as "i", the definition of i = √(-1)
The statement is FALSE; sqrt (-1) = i, a purely imaginary number.
The − 1 is an imaginary number, and therefore not a real number.
The square root of a negative number is not real. Example : √-1
The square root of a negative number is a complex number (not real)
Take the example of iota which is √(-1). Though -1 is very much a real number, iota isn't. It comes under the system of complex numbers.
Negative numbers are real numbers but their square root is an imaginary number..
Proof by counterexample:
Suppose that the square root of any real number is always a real number.
-1 is a real number.
The square root of -1 is i.
Therefore i is a real number.
But i is an imaginary number, not a real number.
Therefore the square root of any real number is not always a real number.
-1 is a real number, but the square root of -1 is i
squar root of -1 is i, that is imaginary number
Write a solution.
both positive and negative are real numbers. the square root of any negative number is not a real number e.g. √16=4 while √-16=4i
the square root of a negative number is a complex number. suppose root square of -1= i
yeah, right. just wanted to point one thing out that the square root of positive real numbers is also a complex number but with its imaginary part being zero.
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Exactly.Real numbers are a subset of Complex Numbers
A square root of a Negative Number is an imaginary .
Real numbers include zero, positive and negative numbers and square root of negative numbers is not real
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The square root of a negative number is not real.