spammers stay away Prove that 3/2root 5 is an irrational number class X
Answers
Step-by-step explanation:
Let us assume that √5 is a rational number.
So it can be expressed in the form p/q where p,q are co-prime integers and q≠0
⇒ √5 = p/q
On squaring both the sides we get,
⇒5 = p²/q²
⇒5q² = p² —————–(i)
p²/5 = q²
So 5 divides p
p is a multiple of 5
⇒ p = 5m
⇒ p² = 25m² ————-(ii)
From equations (i) and (ii), we get,
5q² = 25m²
⇒ q² = 5m²
⇒ q² is a multiple of 5
⇒ q is a multiple of 5
Hence, p,q have a common factor 5. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number
√5 is an irrational number.
Hence proved
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Prove 3+2
5
is irrational.
→ let take that 3+2
5
is rational number
→ so, we can write this answer as
⇒3+2
5
=
b
a
Here a & b use two coprime number and b
=0.
⇒2
5
=
b
a
−3
⇒2
5
=
b
a−3b
∴
5
=
2b
a−3b
Here a and b are integer so
2b
a−3b
is a rational number so
5
should be rational number but
5
is a irrational number so it is contradict
- Hence 3+2
5
is irrational.