Hello Friend!
Rational number between: [tex]7.8 [/tex]
irrational :
If [tex]a\ \textless \ b [/tex], then it follows that 2–√+a<2–√+b, and there exists a rational number r with 2–√+a<r<2–√+b. But then it follows that a<r−2–√<b. What sort of number is r−2–√?
We know that the irrational number could be this: [tex]7[/tex] [tex]1/2 [/tex]or [tex]7.888888888887777777[/tex].
And yes, It can be proven that between any two real numbers there exists a rational number. Therefore there exists a rational number [tex]r[/tex] such that:
7.7+2–√<r<7.9+2–√
By calculator we can find a rational number r that satisfies these condition, I choose [tex]9.2[/tex]. Now subtract square[tex] root 2[/tex].
7.7<9.2−2–√<7.9
So The Answer is between [tex]7.7[/tex] and [tex]7.9[/tex]
Rational number : [tex]7.8[/tex].
Irrational number : 9.2 - √2
Or, a simpler answer would be
Irrational number
[tex]7.81811811181111[/tex]... there is no repeat of period.
So [tex]7.8[/tex] is irrational.
I Hope my answer has come to your Help. Thank you for posting your question here in [tex]Brainly[/tex]. We hope to answer more of your questions and inquiries soon. Have a nice day ahead! :)
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