Proof that root 5 is an …

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Proof that root 5 is an irrational number

Posted by Shofia Jha 5 years, 9 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 9 months ago

Let $\sqrt 5$ is a rational number.
$\sqrt { 5 } = \frac { a } { b }$ (a, b are co-primes and b $\neq$ 0)
or, $a = b \sqrt { 5 }$
On squaring both the sides, we get
a²=5b² ---------------------------------(1)
Hence 5 is a factor of a²
so 5 is a factor of a
Let a = 5c, (c is some integer)
$\therefore$ a² = 25c²

From equation(1) putting the value of a²
or, 5b² = 25c²

or b²=5c²

so 5 is a factor of b²
or 5 is a factor of b
Hence 5 is a common factor of a and b
But this contradicts the fact that a and b are co-primes.

This is because we assumed that $\sqrt 5$ is rational
$\therefore$ $\sqrt 5$ is irrational.

3Thank You

ANSWER

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