Question

3-root5 is a irrational number prove

Answer 1

To ProvE :

3 - √5 is a Irrational number.

SolutioN :

Let's assume 3 - √5 is a Rational number.

$\tt \longmapsto 3 - \sqrt{5} = \dfrac{a}{b}$

$\tt \longmapsto - \sqrt{5} = \dfrac{a}{b} - 3$

$\tt \longmapsto \sqrt{5} = 3 - \dfrac{a}{b}$

$\tt \longmapsto \sqrt{5} = \dfrac{3b - a}{b}$

$\tt\bigstar \: \: \: \: We \: know, \: that \sqrt{5} \: is \: an \: Irrational \\ \tt number. But \frac{3b-a}{b} \: is \: Rational \: number.$

$\tt \dagger \: \: \: \: \: Irrational\neq Rational.$

So, Assumption Was wrong the given number an Irrational.

Hence Proved.

$\rule{200}3$

MorE InformatioN :

• Sum of two different Irrational number always Irrational.
• Product Of two different Irrational also Irrational.
• Example :
• √p + √q.
• √p
• 2 + 3√5, etc.