The root of all evil

Contrary to popular opinion, it's not money. In fact, according to the Bible:

For the love of money is a root of all kinds of evil… (1 Timothy 6:10)

Not money, on it's own, but the love of money. And the love of money is not THE root. It's only a root. And not ALL evil, but all kinds of evil.

This post is not a philosophical or theological post. In fact, it's another mathematical post. In mathematical terms, the statement "Money is not the root of all evil" is Money != √(of all evil), which says Money does not equal (!=) the root (√) of all evil.

So, what exactly is a root? It's basically the opposite of an exponent. From Math Open Reference:

The root of a number x is another number, which when multiplied by itself a given number of times, equals x.

The square root is the most common: the square root of 4 is 2 because 2 x 2 = 4, the square root of 100 is 10, etc. There are roots of any positive integer greater than 1: 3rd roots, 4th roots, etc.

For example, the third root (also called the cube root) of 64 is 4, because if you multiply three fours together you get 64:

4 × 4 × 4 = 64

This would be written as The above would be spoken as "the third root of 64 is 4" or "the cube root of 64 is 4".

• The second root is usually called the "square root".
• The third root of a number is usually called the "cube root",
• After that, they are called the nth root, for example the 5th root, 7th root etc

And these are the symbols that are used in taking roots of numbers:

The symbols

Degree	The number of times the radicand is multiplied by itself. 2 means square root, 3 means cube root. After that they are called the 4th root, 5th root and so on. If this is missing, it is assumed to be 2 - the square root.
Radical symbol	The √ symbol that means "root of". The length of the horizontal bar is important. See note below.
Radicand	The thing you are finding the root of.

 And finally, also related to exponents is the logarithm:

In mathematics, the logarithm is the inverse operation to exponentiation.

But what does that mean?

That means the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number.

Like exponents and roots, logarithms use exponents and a base. (Remember from last week that a fractional exponent is the root of a number). Roots, exponents and logarithms each solve for a different value of the base and exponent:

You can take a logarithm using any base but the most common bases are 10 (called the common logarithm or common log), base 2 (called the binary log) and base e (called the natural log). What is natural about using a letter as the base of a logarithm? Because the number e occurs often in nature, often used for finding the growth or decay of something. And yes, e is a number just like pi is a number...e is approximately equal to 2.718...like pi, e is irrational, it doesn't have an exact value.

Let's look at some examples:

Solving when given the base and exponent: 10^2 = x or 10 x 10 = 100, so 10^2 = 100

Solving for the base when given the exponent: x^2 = 100, you find the square root of both sides...the square root of x^2 = x and the square root of 100 is 10, so 10 = √100

Solving for the exponent when given the root: 10^x = 100...take the common log of both sides you get x = log 100. We can use a log table or a calculator and we'd find that x = 2, so 2 = log 100

Why is a root the same as a fractional exponent? If you remember from last week, a power raised to a power is just the 2 powers multiplied together: 10^2 = 100, now let's get the 10 on the left side alone, we can get rid of the 2 by raising it to the 1/2 power, since 2 x 1/2 = 1, and whatever we do to one side of the equation, we have to do to the other, so 10^2^(1/2) = 100^(1/2) or 10 = 100^(1/2) which means that √100 = 100^(1/2)

I think that's it for math for awhile!

Interesting days

Today - Firefly Day, Go Diaper Free Week and Pig In A Blanket Day

Tomorrow - DNA Day, Malaria Day and Hug A Plumber Day

May will be Golf Month, Hamburger Month, Bike Month, Photo Month, Lyme Disease Awareness Month, Barbecue Month and Get Caught Reading Month!

Next Monday  - Lei Day, School Principals' Day, Purebred Dog Day, School Bus Drivers Day, Mother Goose Day, New Home Owners Day, International Workers' Day and Executive Coaching Day

May 24 - Brother's Day, Tiara Day and Escargot Day