prove that 2√5 in irrational
Answers
Answered by
1
Step-by-step explanation:
If possible, let us assume 2+
5
is a rational number.
2+
5
=
q
p
where p,q∈z,q
=0
2−
q
p
=−
5
q
2q−p
=−
5
⇒−
5
is a rational number
∵
q
2q−p
is a rational number
But −
5
is not a rational number.
∴ Our supposition 2+
5
is a rational number is wrong.
⇒2+
5
is an irrational number.
Answered by
0
Step-by-step explanation:
We conclude that √5 is an irrational number. We can write 2 as 21, thus observing that it is a rational number. We know that a sum of a rational number and an irrational number is an irrational number. Hence, we observe that 2+√5 is an irrational number.
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