find three different irrational number between the rational number 5/7and9/11
Answers
Answer:
Step-by-step explanation:
There are infinitely many irrational numbers between any two real numbers (not just three).
Find any three irrational numbers less than 2, e.g.
π
2
π2
, (I’ll let you find two others), and add them to 5 and to 9. Note that 7–5=2 and 11–9=2, so since your irrationals are less than 2, adding them to 5 and to 9 will put them in the required intervals.
Also remember rational+irrational=irrational always (why? you should be able to prove this).
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Later: I now think you are asking for 3 irrational number between 5/7 and 9/11.
For that, note that 9/11–5/7 = 8/77 which is slightly larger than 1/10, so let’s use
π
100
π100
and add multiples of it to 5/7 giving 3 irrational numbers, namely
5
7
+
π
100
,
5
7
+
2π
100
,
5
7
+
3π
100
57+π100,57+2π100,57+3π100
all lying between 5/7 and 9/11.
Answer:
55/77 and 63/77
rational numbers between them are 56/77 , 57/77 , 58/77 , 59/77, 60/77