Cruz Stathas asked, updated on November 16th, 2021; Topic:
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/amaanswers.com/what-is-the-authors-attitude-toward-a-subject-called-quizlet"> tps://amaanswers.com/how-do-you-simplify-the-square-root-of-99"> ##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.
This is because to square a number just means to multiply it by itself. For example, (-2) squared is (-2)(-2) = 4. Note that this is positive because when you multiply two negative numbers you get a positive result.
Hence, is the square root of negative 2 irrational? Conclusion. The square root of 2 is "irrational" (cannot be written as a fraction) ... because if it could be written as a fraction then we would have the absurd case that the fraction would have even numbers at both top and bottom and so could always be simplified.
As it, what is the square root of a negative 4?
Given the number 4 for example, the square root of 4 could be 2 or it could be -2. The principal square root is the positive one.
Why is i the square root of negative one?
Here, the term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero (which has one double square root).
If the negative sign is inside the parentheses you cube the negative with the number, so (-2)^3 = -8. In this case there is no difference in the answers, but if the exponent were even it would make a difference. For example, -(2)^2 = -4, but (-2)^2 = 4, so the place of the negative would matter.
Specifically, the Greeks discovered that the diagonal of a square whose sides are 1 unit long has a diagonal whose length cannot be rational. By the Pythagorean Theorem, the length of the diagonal equals the square root of 2. So the square root of 2 is irrational!