To see the answer, pass your mouse over the colored area.
To cover the answer again, click "Refresh" ("Reload").
Do the problem yourself first!
The denominator is now rational.
Real numbers
A real number is any number that you would expect to find on the number line. The absolute value of each real number names a distance from 0.
The two main categories of real numbers are rational and irrational. These numbers are the subject of calculus and of scientific measurement.
A real variable is a variable that takes on real values.
Problem 12. Let x be a real variable, and let 3 < x < 4. Name five values that x might have.
For example, 3.1, 3.14, , , .
Problem 13. If the square root is to be a real number, then the radicand may not be negative. (There is no such real number, for example, as .)
If is to be real, then we must have x ≥ 0.
(If you are not viewing this page with Internet Explorer 6, then your browser may not be able to display the symbol ≥, "is greater than or equal to;" or ≤, "is less than or equal to.")
Therefore, what values are permitted to the real variable x ?
a)
x − 3 ≥ 0; that is, x ≥ 3.
b)
1 + x ≥ 0; x ≥ −1.
c)
1 − x ≥ 0; −x ≥ −1, which implies x ≤ 1.
d)
x² ≥ 0. In this case, x may be any real number.
Next Lesson: Simplifying radicals
Table of Contents | Home
Please make a donation to keep TheMathPage online.
Even $1 will help.
Copyright © 2001-2007 Lawrence Spector
Questions or comments?
E-mail: themathpage@nyc.rr.com