   SEARCH HOME Math Central Quandaries & Queries  Question from Jawsh, a student: I don't quite understand the whole idea of rationals. If you have 3Squareroot 49. Is that equal to 3Squareroot 7^2? Can you break it down with an example for me please. Jawsh,

A rational number is almost the same thing as a fraction. The only differences are that some people don't consider "fraction" to include negative fractions such as -3/5 (this distinction is made more in junior high school than elsewhere), and a rational number is independent of how it's represented so that 1/2, 3/6, and 0.5 are all the same rational number. (Technically the first two are equivalent fractions but not the same fraction; and the third is not a fraction but a terminating decimal, representing the decimal fraction 5/10. However, we may use the equals sign between them even if we call them fractions. Every rational number has a "main" fraction representing it, namely the fraction in lowest terms.)

If a is positive (or 0) √(a2) = a
If a is negative, √(a2) = |a| = -a (which is bigger than 0)

So 3 √(49) = 3 √(72) = 3 × 7 = 21

Good Hunting!
RD     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.