Math CentralQuandaries & 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.


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!


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