# Difference between Exponents and Roots

• Mar 30th 2005, 12:51 PM
Math Buddy
Difference between Exponents and Roots
I have a question that asks me to describe what the difference between exponents and roots (if there is any). So what is the difference?
• Mar 30th 2005, 04:38 PM
MathGuru
The Difference is negligable
Hi Math Buddy, welcome to MHF.

The truth is that you can represent any root in the form of an exponent

for example the square root of 2 is also 2 raised to the power of (1/2).

Or SQRT(2) = 2^(1/2)

Math Guru
• Mar 31st 2005, 03:43 PM
Math Buddy
Thnk you Math Guru
The teacher was very impressed with my (actually your) answer. She asked my how I knew that and I told her about your forum.

Thanks Math Guru,

Math Buddy
• Apr 9th 2005, 04:17 AM
theprof
Quote:

Originally Posted by Math Buddy
I have a question that asks me to describe what the difference between exponents and roots (if there is any). So what is the difference?

none, if you trust in fractionals
Look at this

in natural numbers (0,1,2,3,4...)
x^2=4 means x=2, because 2^2=4

and if I loook for an exponent that gives me

4^x = 2?

How much is x?

not 1 because 4^1 = 4
not 0 because 4^0 = 1

something in between, but how much?
Remember power laws:

(3^4)^5 = 3^20

4^x=2 needs that x is... 0.5!
so 4^(1/2) is the same that sqrt(4), that is 2.

bye

hope this helps
• Jun 23rd 2005, 10:50 PM
tbsmith
I think that the difference between an exponent and a root is that an exponent is a value used as a power to which another value is raised and a root is a number that, when multiplied by itself an appropriate number of times, returns the value under the radical.