1. Prove that √√5 is irrational. 2. Prove that 3 + 2√5 is irrational. 3. Prove that the following are irrationals : (i) √/2 (ii) 7√5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Rearranging, we get 2
3b
Since 3, a and b are integers,
is rational, and
3b
a
But this contradicts the fact that 2 is irrational
So, we conclude that 3/2 is irrational.
to
EXERCISE 1
1. Prove that V5 is irrational.
2. Prove that 3+ 2/5 is irrational.
3. Prove that the following are irrationals:
(i)
(ii) 75
(i)
2020-21
Transcribed Image Text:Rearranging, we get 2 3b Since 3, a and b are integers, is rational, and 3b a But this contradicts the fact that 2 is irrational So, we conclude that 3/2 is irrational. to EXERCISE 1 1. Prove that V5 is irrational. 2. Prove that 3+ 2/5 is irrational. 3. Prove that the following are irrationals: (i) (ii) 75 (i) 2020-21
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