prove root 5 is irrational. those who answer correct will get brainliest
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Answer:
Solution:
Let us prove that √5 is an irrational number.
This question can be proved with the help of the contradiction method. Let's assume that √5 is a rational number. If √5 is rational, that means it can be written in the form of a/b, where a and b integers that have no common factor other than 1 and b ≠ 0.
√5/1 = a/b
√5b = a
Squaring both sides,
5b² = a²
b² = a²/5 --- (1)
This means 5 divides a².
That means it also divides a.
a/5 = c
a = 5c
On squaring, we get
a² = 25c²
Put the value of a² in equation (1).
5b² = 25c²
b² = 5c²
b²/5 = c²
This means b² is divisible by 5 and so b is also divisible by 5. Therefore, a and b have 5 as a common factor. But this contradicts the fact that a and b are coprime. This contradiction has arisen because of our incorrect assumption that √5 is a rational number. So, we conclude that √5 is irrational.
Step-by-step explanation: