can we square root a negative number ?

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can we square root a negative number ?

Here are some links that might be useful to you:

https://math.stackexchange.com/questions/677619/why-is-the-square-root-of-a-negative-number-impossible

https://math.stackexchange.com/questions/677619/why-is-the-square-root-of-a-negative-number-impossible
Why is the square root of a negative number impossible?
The result of multiplication of same numbers is always a positive number. If we take square root of a negative number, we should place the negative sign before radical sign/radix -√, e.g. imaginary number √-1 = -√1. You do not need sci-fi to be convinced because its roots are -1 = -1 x 1 = 1 x -1 or – (1 x 1) = -(-1 x -1). Simple and logical.

https://www.themathdoctors.org/squares-roots-and-negative-numbers

https://www.themathdoctors.org/squares-roots-and-negative-numbers
Squares, Roots, and Negative Numbers – The Math Doctors
27 oct. 2023while solving equations we do as follows. x 2 = 4. taking square root on both sides we get. √ (x 2) = √4. or, x = ±2. When you wrote √4 = ±2, you really meant that there are two numbers whose square is 4, namely 2 and -2. Using the square-root sign was sort of a shorthand for what you were thinking.

https://www.youtube.com / watch?v=BkxCfa5CDe4

https://www.youtube.com / watch?v=BkxCfa5CDe4
How To Find The Square Root of a Negative Number – YouTube
This video explains how to find the square root of a negative number.Square Roots and Cube Roots: https://www.youtube.com/watch?v=IW…

https://mathbitsnotebook.com/Algebra1/Radicals/RADNegativeUnder.html

https://mathbitsnotebook.com/Algebra1/Radicals/RADNegativeUnder.html
Negative Value Under the Square Root Radical – MathBitsNotebook
Difficulties, however, develop when we look at a problem such as . This square root problem is asking for a number multiplied times itself that will give a product (answer) of -16. There simply is no way to multiply a number times itself and get a negative result. Consider: (4) • (4) = 16 and (-4) • (-4) = 16.

https://www.mathsisfun.com/square-root.html

https://www.mathsisfun.com/square-root.html
Squares and Square Roots – Math is Fun
Calculating Square Roots. It is easy to work out the square root of a perfect square, but it is really hard to work out other square roots. Example: what is √10? Well, 3 × 3 = 9 and 4 × 4 = 16, so we can guess the answer is between 3 and 4. Let’s try 3.5: 3.5 × 3.5 = 12.25. Let’s try 3.2: 3.2 × 3.2 = 10.24.

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/v/imaginary-roots-of-negative-numbers

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/v/imaginary-roots-of-negative-numbers
Simplifying roots of negative numbers (video) | Khan Academy
That we can actually put, input, negative numbers in the domain of this function. That we can actually get imaginary, or complex, results. So we can rewrite negative 52 as negative 1 times 52. So this can be rewritten as the principal square root of negative 1 times 52. And then, if we assume that this is the principal branch of the complex …

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:radicals/v/introduction-to-square-roots

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:radicals/v/introduction-to-square-roots
Intro to square roots (video) | Radicals | Khan Academy
Yes, square roots can create 2 answers — the positive (principal) root and the negative root. When you are working with square roots in an expression, you need to know which value you are expected to use. The default is the principal root. We only use the negative root when there is a minus in front of the radical. For example: 8 + sqrt (9) = 11.

https://study.com/academy/lesson/negative-square-root-definition-lesson-quiz.html

https://study.com/academy/lesson/negative-square-root-definition-lesson-quiz.html
Negative Square Root | Definition & Examples – Lesson | Study.com
21 nov. 2023However, square roots can also be negative. Thus, the number -6 can be a square root of the number 36, just not a principal square root. So the negative square root is the same number as the …

https://www.onemathematicalcat.org/Math/Precalculus_obj/squareRootNeg.htm

https://www.onemathematicalcat.org/Math/Precalculus_obj/squareRootNeg.htm
The Square Root of a Negative Number – OneMathematicalCat.org
23 juin 2023Complex numbers allow us to compute the square root of negative numbers, like √− 4. Remember the key fact: i: = √− 1, so that i2 = − 1. Let p be a positive real number, so that − p is a negative real number. Then: (Note: When the distinction becomes important in higher-level mathematics, then √− p is called the principal …

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-roots/a/square-roots-review

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-roots/a/square-roots-review
Square roots review (article) | Khan Academy
The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is 1 . Finding the square root of a number is the opposite of squaring a number. Example: 4 × 4 or 4 2 = 16. So 16 = 4. If the square root is a whole number, it is called a perfect square!
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