What is a 'square root' and a 'real number'?

Question

I am reviewing my high school math and I seem to not remember the basics!

Answer 1

hmmm...
square root of a number is the number that you need to square (multiply by itself) to get to the first number

for example squareroot(64)=8
because 8x8=64

a few, called perfect sqaures can be figured out without much thought, but others, like say the square root of 2 are a bit more difficult.

here is an excerpt from:
Russell, Bertrand. A History of Western Philosophy. New York: Touchstone, 1972.

"The square root of 2, which was the first irrational to be discovered, was known to the early Pythagoreans, and ingenious methods of approximating to its value were discovered. The best was as follows: Form two columns of numbers, which we will call the "a"'s and the "b"'s; each starts with "1". The next "a", at each stage is formed by adding the last "a" and "b" already obtained; the next "b" is formed by adding twice the previousa to the previous "b".
The first 6 pairs so obtained are
(1,), (2,3), (5,7), (12,17), (29,41), (70,99)
In each pair, 2a(squared)-b(squared) is 1 or -1. Thus b/a is nearly the square root of 2, and at each fresh step it gets nearer. For instance, the reader may satisfy himself that the square of 99/70 is very nearly equal to 2."

so thats that for square roots...
and real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2.4871773339…. ... (quote from en.wikipedia.org/wiki/Real number)

I hope I helped :D
gotta love math

Answer 2

The square root of a number is a number that we can multiply with itself to get the number we started off with. An example will make this clearer. The square root of 9 is 3, because 3 x 3 = 9.
Because of some rules of algebra, each number actually has 2 square roots, but these are the same except for their sign. So going back to the example above, the square roots of 9 are actually 3 and -3 because if we look at -3 * -3, the minuses cancel and we again get 9.

All of the numbers that you will deal with in elementary maths will be real numbers. A simple way of defining the real numbers is to say that every point on the numberline represents a real number. There is an infinite number of real numbers, and there are many more real numbers than counting numbers. In case you are interested, real numbers have such an odd name to contrast them with "imaginary" numbers that come up in some higher mathematics.

Best of luck!

Answer 3

Square Root
In mathematics, a square root of a number x is a number r such that r^2 = x, or in words, a number r whose square (the result of multiplying the number by itself) is x. Every non-negative real number x has a unique non-negative square root, called the principal square root and denoted with a radical symbol as '√x' . For example, the principal square root of 9 is 3, denoted √9 = 3 , because 3^2 = 3 x 3 = 9 . The other square root of 9 is −3.

Real Number
In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2.4871773339…. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as π and the square root of 2, and can be represented as points along an infinitely long number line.

Answer 4

The square root of x is a number that, when multiplied by itself, equals x.
For example, the square root of 9 is 3 (or -3) because 3X3 (or -3X-3) = 9.
The square root of 16 is 4 (or -4) because 4X4 (or -4X-4) = 16.

Geometrically, the square root is the length of the side of a square. (The larger number is the area.)
So if you had a square with an area of 25, the root (length of one side) would be 5.

A real number is any number that is not "imaginary." An imaginary number is the square root of a negative number.

Answer 5

A square root is the inverse operation to squaring a number.

A real number is any number that does not contain an imaginary component, which is a number that contains the square root of a negative number (often represented as an "i" or a "j").

Answer 6

a real number is any number from negative infinity to infinity

a square root is the inverse function of squaring a number, basically, its wat number multiplied by it self gives the number u started with