Square Real Root

Algebra Level 1

True or false?

The square root of any real number is always a real number.

False True

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18 solutions

Alex Li
Jul 1, 2015

The square root of a negative number is not real.

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.

Niklas Jansson - 5 years, 1 month ago

Exactly! The answer is a Imaginary Number.

Victor Paes Plinio - 5 years, 11 months ago

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You guys be talking crazy. Can't wait to tell my boys you think there's imaginary numbers.

Michael Wilbur - 5 years, 5 months ago

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A very famous mathematician regarded that name as inappropriate. He preferred calling them lateral numbers.

Felix Castrillon - 5 years, 2 months ago

Dude its simple algebra your boys probably already know about them if they are in the 6th grade or higher....

Matt Rouse - 5 years ago

may or may not be.

Amna Mushtaq - 5 years, 8 months ago
Alec Camhi
Jul 3, 2015

Real numbers can be negative, and negative numbers have imaginary square roots. For example, 1 = i \sqrt{-1} = i

The square root of a negative number is imaginary.

Danish Mahmood
Jul 5, 2015

its answer is false because all negative integer also included in real number so square root of a negative number is always complex

Eric Schoen
Jul 3, 2015

The square root of any negative number is imaginary. Notated as "i", the definition of i = √(-1)

Shashank Rustagi
Jul 3, 2015

The statement is FALSE; sqrt (-1) = i, a purely imaginary number.

Keshav Ramesh
Feb 13, 2017

The 1 \sqrt{-1} is an imaginary number, and therefore not a real number.

Vector Purba
Oct 12, 2016

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.

Cnu Reddy
Jul 6, 2015

Negative numbers are real numbers but their square root is an imaginary number..

Scott Calo
Jul 5, 2015

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.

Zach Glover
Jul 5, 2015

-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.

Usama Ejaz
Jul 4, 2015

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

Atika Samiha
Jul 3, 2015

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.

Anindya Mahajan - 5 years, 11 months ago

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Exactly.Real numbers are a subset of Complex Numbers

Abdur Rehman Zahid - 5 years, 11 months ago
Adrian Joshua
Jul 3, 2015

A square root of a Negative Number is an imaginary .

Arjun Pailoor
Jul 3, 2015

Real numbers include zero, positive and negative numbers and square root of negative numbers is not real

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