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How do you rationalize denominator surds?
An example may help. If you have the fraction 1 / (2 + root(3)), where root() is the square root function, you multiply top and bottom by (2 - root(3)). If you multiply everything out, you will have no square root in the denominator, instead, you will have a square root in the numerator. If the denominator is only a root, eg root(3), you multiply top and bottom by root(3).
What is a cube root function?
The cube root function is the inverse of the cube function. So, given a number y, the cube root function seeks to find a number, x, such that multiplying 1 by that number 3 times gives y. [Note that this is equivalent to multiplying the number by itself two times, not three.] That is, cuberoot(y) = x <=> x^3 = y For example, 2*2*2 = 8 so the cube root of 8 is 2. 1.5^3 = 3.375 so the cube root of 3.375 is 1.5 (-3)^3 = -27 so the cube root of -27 is -3. The cube root of y is denoted by y^(1/3). It can also be written using the radical symbol like for a square-root, but the radical must be preceded by a superscript 3. Apologies, but this browser is crap and so I cannot show that representation.
What is an example of real life square root function?
electricians use the Square Root function when connecting 3 way outlets with the electral current of an intel processor.
How does inverse function work?
Let's illustrate with an example. The square function takes a number as its input, and returns the square of a number. The opposite (inverse) function is the square root (input: any non-negative number; output: the square root). For example, the square of 3 is 9; the square root of 9 is 3. The idea, then, is that if you apply first a function, then its inverse, you get the original number back.
Why root 2 is smaller than 3 root 4?
This is because the square root function, with the range defined as the non-negative real numbers, is monotonic increasing throughout.
