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Mathematics 16 Online
OpenStudy (anonymous):

Which number is not Rational?

OpenStudy (anonymous):

Much numbers !

OpenStudy (anonymous):

\[\sqrt{3}\] 0.25 1/5 \[\sqrt{9}\]

OpenStudy (anonymous):

Many numbers bro, just anything with unlimited decimals are irrational. Like pi or 1/3

OpenStudy (anonymous):

those numbers

OpenStudy (anonymous):

Aha ! \[\sqrt{9}=?\]

OpenStudy (anonymous):

what?

OpenStudy (anonymous):

3

OpenStudy (anonymous):

The D = ???

OpenStudy (anonymous):

root 3

OpenStudy (anonymous):

As long as it is finite it is rational, hence infinite decimals are irrational. Like pi, which goes on unlimited but 1/2 is rational because it stops at .5

OpenStudy (anonymous):

d is the answer?

OpenStudy (anonymous):

wait why is 3 not rational?

OpenStudy (anonymous):

Type it in a calculator and see, whichever has way too many decimals to fit, it is irrational

OpenStudy (anonymous):

No ! We say : Rational numbers are this : R:{a/b|a,b in Z and isnt b= 0 } k ?

OpenStudy (anonymous):

ok im confused!?!?!

OpenStudy (anonymous):

@Hero

OpenStudy (anonymous):

@Hero these people are confusing me

OpenStudy (anonymous):

Bro, rational numbers just mean it could be represented as a fraction or no decimal place number. That's it man, anything with reoccuring or repeating decimals, that's the shtuff that's irrational

OpenStudy (anonymous):

root 3 is irrational bcoz it cannot be expressed as a ratio od two coprime poitive integers

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

while the res of them can be expressed.even root 9 is equal to + or - 3

OpenStudy (anonymous):

look : In 2 : 0.25 is Rational . In 3 : 1/5 is Rational . In 4 : \[\sqrt{9}\] = 3 So in 1 can u say how is : \[\sqrt{3}=????\] So its Rational . Got it ?:)

OpenStudy (anonymous):

ok still confused

hero (hero):

If a number is rational, it can be expressed in the form \(\dfrac{a}{b}\) \(0.25 = \dfrac{1}{4}\) \(\dfrac{1}{5} = \dfrac{1}{5}\) \(\sqrt{9} = 3 = \dfrac{6}{2}\) @PvtGunner, Can we express \(\sqrt{3}\) in rational form?

OpenStudy (anonymous):

No

hero (hero):

Why not?

hero (hero):

a and b must be real number integers by the way.

OpenStudy (anonymous):

Because \[\sqrt{3}\] can only be a decimal

OpenStudy (anonymous):

right?

hero (hero):

Well, at the moment it is in irrational form, not decimal form. In decimal form, the value of \(\sqrt{3}\) can only be approximated. Nevertheless we are unable to express it in rational form. And reason is simply because \(\sqrt{3}\) is an irrational number.

OpenStudy (anonymous):

OHHH ok i get it thank you @Hero

OpenStudy (anonymous):

so basically if it is rational it can be written as a fraction and if not rational it cant be written as a fraction

OpenStudy (anonymous):

@Hero

hero (hero):

Well, \(\dfrac{\sqrt{3}}{1}\) is a fraction and it equals \(\sqrt{3}\) \(\dfrac{2\sqrt{3}}{2} = \sqrt{3}\) and it is also a fraction. What makes a rational number \(\dfrac{a}{b}\) unique is that a and b must be integers.

OpenStudy (anonymous):

ok that makes sense

OpenStudy (anonymous):

so the anwser is\[\sqrt{3}\]

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