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What do you think is true of the square roots of a complex number?
Wiki User
∙ 13y ago
I posted an answer about cube roots of complex numbers. The same info can be applied to square roots. (see related links)
Wiki User
∙ 13y ago
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What is square root-?
I think you mean square root. The square root of a number is that number when multiplied by itself will give the original number. For example the original number is 4, then we know that 2 x 2 is 4, hence 2 is the square root of 4. We also know that -2 x -2 is also 4, hence 4 has two square roots, +2 and -2 Similarly 9 has two square roots, +3, and -3 Similarly 16 has two square roots, +4, and -4 Not all numbers have such whole numbers for their square roots. For example the square roots of 2 are nearly equal to +1.4142 and -1.4142. Similarly the square roots of 3 are nearly equal to +1.73205 and -1.73205
What is the square of 256?
If you think squares and square roots are the same thing, you're mistaken. They are the same type of thing, but opposites. When you find the square of a number, you multiply it twice by itself. Square roots are when you find what number an be squared to get this number. So, the answer would be 19,456. I'm in 7th grade and I know that. Oh no, I wrote more numbers. Sorry to you mathematically challenged people who seem to have a problem comprehending those.
Is a non perfect square root a rational number?
It can be. The square roots of 2.25 are -1.5 and 1.5: rational numbers.
What is the number that the complex sunflower is on?
I think you're referring to the Fibonacci sequence.
What is the square root of 175?
The square root of 175 is: ± 13.228757 13.23 (rounded)
Why do square roots come in pairs but cubed roots don't?
The square of a negative number is the same as the square of its positive counterpart, aka its additive inverse ( [-2]2 = 22 = 4), so every positive number has two square roots, a positive one and negative one (both 2 and -2 are square roots of 4). However, the cube of any number will always have the same sign as the original number (23 = 8, [-2]3 = -8). This all follows from simple arithmetic with signs. The product of any two negative numbers is positive, as is the product of any two positive numbers, while the product of a negative number and a positive number is negative. All squares, by definition, are the product of either two positive numbers or two negative numbers, and in either case, the product must be positive. But a cube is the product of a number and its square (x3 = x * x * x = x2 * x). But we already know that the square must be positive, whether original number is positive or negative. So the sign of the original number determines the sign of the cube (because a positive number times a positive number is positive and a positive number times a negative number is negative). If you apply that rule in reverse, then the sign of the cube root must be the same as the sign of the number you are taking the cube root of. Think of it this way. If you are trying to calculate the square root of a number, y, you are looking for another number, x, for which it is true that x * x = y. For any positive number y, there are always two values of x that satisfy that equation, with one being positive and the other being negative, but both having the same absolute value. And therefore, every positive number has two square roots. On the other hand, if you are trying to find the cube root of a number, y, you are looking for a number, z, for which it is true that z * z * z = y. For any number, y, either positive or negative, there will be only one value of z that satisfies that equation. Therefore, every number, positive or negative, has just one cube root. Actually, technically, once you get into higher mathematics, what is really going on is that every number has 3 cube roots, but they all just happen to have the same value. In fact, for any "degree" of root (square root, cube root, 4th root, 5th root, ... 100th root, ...) the number of roots of a number is exactly equal to the degree of the root (a number will have 4 4th roots, 5 5th roots, 10 10th roots, 99 99th roots, etc.) But, if the degree of the root is odd, then all of the roots will have the same value, while if the degree is even, the roots will be evenly split between two values that are the additive inverses of each other. For example, the 5th roots of -243 are -3, -3, -3, -3, and -3, while the 6th roots of 64 are 2, 2, 2, -2, -2, and -2. Note also that negative numbers cannot have any roots of any even degree (square roots, 4th roots, 6th roots, etc.) Actually, even that's not true when you get into really advanced math. Even negative numbers have even-degree roots, it's just that the roots are not real numbers. They are "imaginary" numbers. This is, I'm sure, way beyond your level of education in mathematics, and I'm not trying to confuse you. But if I hadn't included these last two paragraphs, some wise-guy mathematician would come along and "correct" me, and in the process probably confuse you even more. For your purposes, however, just ignore the last two paragraphs.
Does the number 5 always have to be in the middle of a magic square?
Think! What if the magic square had an even number of cells. There's your answer.
What is a number called when it is not prime and not a square number?
I think there just called numbers quote the words i think
What is the 4th square number?
16 i think :S
What you get a whole number when taking the square root of a number it's called a...?
I think the answer to this poorly phrased question is "a perfect square".
How many complex number solutions can exist for a quadratic equation?
Quadratic equations always have 2 solutions. The solutions may be 2 real numbers (think of a parabola crossing the x axis at 2 different points) or it could have a "double root" real solution (think of a parabola just touching the x-axis at its vertex), or it can have complex roots (which will be complex conjugates of each other). For the last scenario, the graph of the parabola will not touch the x axis.
Is pi a complex number?
The set of real numbers are a subset of the set of complex numbers: imagine the complex plane with real numbers existing on the horizontal number line, and pure imaginary existing on the vertical axis. The entire plane (which includes both axes) is the set of complex numbers. So any real number (such as pi) will also be a complex number. But many people think of complex numbers as something that is "not a real number".
