Posts Tagged ‘square root’
Friday, October 2nd, 2009
Definition of the Index of a Radical Expression
Description
A detailed tutorial on the definition of the index of a radical expression. Step by step tutorial including several examples of the index of a radical expression for reference.
Overview
A radical expression is what most people know as a square root. The number, variable, or expression inside the square root symbol is referred to as the radicand. What some of you may not realize is that not only are there square roots, there are cube roots, and several other types of roots. These are the exact opposite functions of the exponents. A square root should technically have a little number two on the outside left of the square root symbol. A cube root would have a three there – any number can go there. That is the index.
Tags: arithmetic, cube root, exponent, expression, index, Math, radical, radicand, root, square root, symbol
Posted in Arithmetic | No Comments »
Thursday, October 1st, 2009
Identifying the Radicand
Description
A detailed tutorial on identifying the radicand. Step by step tutorial including several examples of how to identify the radicand for reference.
Overview
The radicand is associated with what we know as a square root. However, there is a common misconception that a radicand and a square root are the same thing, and they are not. A square root is the entire number – the square root symbol, the number inside, and whatever number it equals. A radicand is simply the number that is inside the square root symbol. For example, take the expression ![\scriptstyle \sqrt[n]{ab+2}](http://s.wordpress.com/latex.php?latex=%5Cscriptstyle%20%5Csqrt%5Bn%5D%7Bab%2B2%7D&bg=ffffff&fg=000000&s=0 "\scriptstyle \sqrt[n]{ab+2}")
. In this expression, the radicand is ab + 2, because that is what we are taking the square root of.
Tags: algebra, exponent, integer, Math, number, perfect square, radicand, ratio, real number, square, square root, symbol
Posted in Algebra | No Comments »
Friday, September 25th, 2009
How to Find the Domain & Range of a Function
Description
A detailed tutorial on finding the domain and range of a function. Step by step tutorial including several examples of how to find the domain and range of a function for reference.
Overview
Finding the domain and range is very important when given the graph of a function. The domain is the set of all possible x values of the function, and the range is the set of all possible y values of the function. When given a function, the first one you want to find is the domain. You want to figure out what is allowed for the x value. Typically, the domain ends up being the set of all real numbers, expressed a R. If the x is found in a fraction, it can be the set of all real numbers excluding 0. If the x is found in a square root, it is the set of all real positive numbers. It’s rare for there to only be a few values allowed for the domain. The next one you want to find is range. Very often, range also ends up being the set of all real numbers. But say you know that something has to come out negative, then it would only be the set of all negative numbers. Each function is a little bit different, but finding the domain and range is typically a very straightforward process.
Tags: algebra, domain, fraction, function, graph, Math, negative, positive, possible, range, real numbers, set, square root, values, x, y
Posted in Algebra | No Comments »
Tuesday, September 22nd, 2009
Cauchy-Schwarz Inequality Explained
Description
A detailed tutorial on the solving of the Cauchy-Schwarz Inequality. Step by step tutorial including several examples of how to solve the Cauchy-Schwarz Inequality for reference.
Overview
The Cauchy-Schwarz Inequality is also known as the Schwarz Inequality, the Bunyakovsky Inequality, and the Cauchy-Bunyakovsky-Schwarz Inequality. It was published by Augustin Cauchy and was first stated by Viktor Yakovlevich Bunyakovsky. It was later rediscovered by Hermann Amandus Schwarz. This is used mostly in linear algebra, when solving vectors. It is also used in probability theory.
The Cauchy-Schwarz Inequality states that for all vectors x and y of an inner product space, 
By taking the square root of both sides, it can be written as 
If the two sides are equal, and if x and y are both independent, then the formula may be restated as 
Tags: Augustin Cauchy, Bunyakovsky Inequality, Cauchy-Bunyakovsky-Schwarz Inequality, Cauchy-Schwarz Inequality, Hermann Amandus Schwarz, inequality, linear algebra, Math, probability theory, product space, Schwarz Inequality, square root, vectors, Viktor Yakovlevich Bunyakovsky
Posted in Algebra | No Comments »
Friday, September 18th, 2009
Introduction to Irrational Numbers
Description
A detailed tutorial on the definition of an irrational number. Step by step tutorial including several examples of irrational numbers for reference.
Overview
An irrational number is a number that cannot be written as the ratio of 2 integers. However, this does not mean they have no place on a number line. One of the most famous irrational numbers is pi, which is approximately equal to 3.14 – however, this is just a simplified version of the actual number. Another famous irrational number is the square root of 2. This is equal to around 1.41. Both irrational numbers and rational numbers are real numbers, which include all integers.
Tags: arithmetic, imaginary, integers, irrational, Math, natural, number, numbers, pi, ratio, rational, real, sqrt(2), square root
Posted in Arithmetic | No Comments »
Friday, September 11th, 2009
An Introduction to Imaginary Numbers
Description
A detailed tutorial on imaginary numbers. Step by step tutorial including several examples of how to solve problems using imaginary numbers for reference.
Overview
An imaginary number is a number that is considered to not be real – for instance, the square root of a negative number. You could never take a square root of a negative number – until you met i. i stands for “imaginary”, and it is the square root of negative one. Many previously impossible problems can now be solved by pulling out i from the equation.
Tags: -1, algebra, i, imaginary, imaginary number, Math, negative, real, real number, sqrt(-1), square root
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Thursday, September 10th, 2009
How to solve Square Roots
Description
A detailed tutorial on the solving of Square Roots. Step by step tutorial including several examples of how to solve Square Roots for reference. This video demonstrates how to calculate a Square Root by hand with no calculator.
Overview
A square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square (the result of multiplying the number by itself) is x. Square roots of intergers that are not perfect squares are always irrational numbers.
Tags: arithmetic, Math, square root
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Thursday, September 10th, 2009
A Guide to Completing the Square
Description
This video is a tutorial 0n how to solve quadratic equations by completing the square. Two example problems are provided in the video and worked through. The entire process of completing the square is explained in this video.
Overview
A quadratic equation is probably the most well-known type of math problem, following the form ax^2 + bx + c = 0. Most people already know one way of solving these types of equations – the quadratic formula. But the quadratic formula is only one of 3 methods that can be used. The method discussed here is completing the square. Completing the square is when you turn an equation into a squared binomial in order to solve it. You need to remember this:
(x + a)^2 = x^2 + 2ax + a^2
You need to make your equation match up to this. Take the middle term and divide it by 2. That number is a. Square a – if you get the number on your trinomial, then this is a perfect square. You want it to be a perfect square. If it is not, you must get rid of the number on the end and move it to the other side by addition or subtraction. Then you will need to replace the number with a^2 – you will add this to both sides. You find out the value of a the same way you did earlier. You will eventually come up with something that looks like this:
(x + a)^2 = n
Now you will take the square root of both sides, and subtract a from both sides. Then you will be left with x, and it will tell you what x equal. Remember, when taking a square root you must put plus/minus in front of the square root! Just like in the quadratic formula, you need a +/- in your answer.
Tags: algebra, binomials, completing the square, Math, quadratic equation, square, square root, trinomial
Posted in Algebra | No Comments »
