 # What is the square root of a negative number?

Cruz Stathas asked, updated on November 16th, 2021; Topic: square root
👁 545 👍 23 ★★★★☆4.7
/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.

At any event, what is the square of negative 2?

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).

### How do you square root a negative number on a calculator?

How to Calculate the Square Root of:
• A Positive Number: The square root of a positive number can be calculated by: ...
• A Negative Number: To calculate the square root of a negative number, find the square root of the same positive number and multiply by "i". ( ...
• An Imaginary Number: ...
• A Complex Number:

### What is the square of negative 3?

If you want to say "the square of negative three" you write (−3)2.

### What is a negative to the power of 2?

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.

### How do you prove √ 2 is irrational?

Euclid's proof starts with the assumption that √2 is equal to a rational number p/q.
• √2=p/q. Squaring both sides,
• 2=p²/q² The equation can be rewritten as.
• 2q²=p² From this equation, we know p² must be even (since it is 2 multiplied by some number). ...
• 2q²=p²=(2m)²=4m² or. ...
• q²=2m² ...
• √2=p/q=2m/2n. ...
• √2=m/n.
• ### Why is root two irrational?

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!

### What is 2i equal to?

i2 is equal to -1, a real number!

### What is negative I equal to?

Unit Imaginary Number The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. In mathematics the symbol for √(−1) is i for imaginary.
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