# Rational algebraic expressions

• Jan 2nd 2006, 01:31 AM
DenMac21
Rational algebraic expressions
In a book stands that rational algebraic expression is $\displaystyle {\sqrt 2}$ and that are not rational algebraic expression $\displaystyle {\sqrt 2gh}, x+{\sqrt x}$

How can $\displaystyle {\sqrt 2}$ be rational algebraic expression? Why isn't irrational?

Why $\displaystyle {\sqrt 2gh}, x+{\sqrt x}$ are irrational?
• Jan 2nd 2006, 02:05 PM
CaptainBlack
Quote:

Originally Posted by DenMac21
In a book stands that rational algebraic expression is $\displaystyle {\sqrt 2}$ and that are not rational algebraic expression $\displaystyle {\sqrt 2gh}, x+{\sqrt x}$

How can $\displaystyle {\sqrt 2}$ be rational algebraic expression? Why isn't irrational?

Why $\displaystyle {\sqrt 2gh}, x+{\sqrt x}$ are irrational?

A rational algebraic expression is an expressions which is of the form

$\displaystyle \frac{P(x)}{Q(x)}$,

where $\displaystyle P(x)$ and $\displaystyle Q(x)$ are polynomials in x. Note this does not require
that the coefficients in either polynomial be rational.

With this definition $\displaystyle {\sqrt 2}$ is a rational algebraic expression
(even though $\displaystyle {\sqrt 2}$ is not a rational number).

Clearly with this definition $\displaystyle x+{\sqrt x}$ is not a rational algebraic expression.

Assuming the remaining expression should be: $\displaystyle \sqrt {2gh}$ and that $\displaystyle g$ and $\displaystyle h$
are polynomials then this is not a rational algebraic expression.

RonL