Is 9.0 Rational Or Irrational

Amy M.

asked • 08/22/12

Why is -9 non an irrational number?

According to my algebra instructor, all irrational numbers are numbers that do not have square roots that are even? Co-ordinate to what I've constitute online, irrational numbers cannot exist written every bit a simple fraction. -9 is a whole number and therefore tin can be converted into a simple fraction, right? But it has no square root? Dislocated!

3 Answers Past Skillful Tutors

-9 is not an irrational number due to a few things.

First, allow'southward take a wait at the definition of a rational and irrational number.

The definition of a rational number is equally follows:

Any number that can be written equally a fraction with integers

The definition of an irrational number is this:

A existent number that cannot exist expressed in the form of a/b, (where b cannot equal 0). In decimal form, it either never terminates or repeats itself.

So allow's take a await at -9 with these ii definitions in heed,

What can nosotros do to the -9 to arrive a fraction?

Nosotros tin can divide it by ane so at present it looks like this, -9/1.

Which of the two definitions all-time describes this number now?

I hope that I have explained this fairly for your understanding.

Irwin Due south. answered • 08/22/12

Computer and school subjects slowed down to your learning speed

The answer to your question on why -9 has no square root is farther along in your studies, where you lot volition acquire to deal with the world of circuitous numbers.

The problem y'all are encountering is that there is no number that can exist multiplied by itself to go -9, because if you lot remember multiplying like signs always give a positive number.

Not to leave y'all in the dark till so, the foursquare root of -9, is 3i , the letter i letting us know it's not a real number, in fact it'south imaginary!

Most calculators are not set up to process imaginary numbers, then they simply put the word "Mistake" on the screen, which is why it seems to not take a square root.

So in all truth using -9 is non a great case for the proof of irrational/rational numbers, as information technology is neither.

(since the number to be squared to become -9, and the foursquare root of -9 are not "real" numbers, and a number has to accept a "Real" root to be part of the irrational/rational test you lot describe.)

Susan H. answered • 08/22/12

High Schoolhouse/College level Math Tutor

∏I see where your confusion is coming from - in that location is a missing "piece" in your explanation from your instructor - a rational number, when squared, has even exponents. This is a difficult definition to follow, but lets run across if I can requite you an example.

2 is rational; iiⁱⁱ is it's foursquare, and information technology'south exponent is an even number (ii)

√2 is irrational; two¹ is information technology's foursquare, and the exponent here is an odd number (1)

√8 is irrational; iiⁱⁱⁱ (=viii) is it'due south square, and the exponent hither is an odd number (3)

The more common definition used is the one listed to a higher place by Katlin - a rational number is any number which can be written equally a ratio, or fraction (a/b).

Irrational numbers are made upwardly of square roots (other than the square roots of perfect squares, similar four, sixteen, etc), higher gild roots, the number pi, e, etc.

Hopefully that connects the dots between what you heard in class, and how to effigy this out on your own!