Prove that

[tex] \sqrt{5} [/tex]

is an irrational number

# Prove that

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[tex] \sqrt{5} [/tex]

is an irrational number

Prove that

[tex] \sqrt{5} [/tex]

is an irrational number

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[tex]\huge{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\fcolorbox{red}{black}{\red{Answer}}}}}}}}}}}}}}}}}}}[/tex]

Let us assume√5 is rational.

√5=[tex]\frac{p}{q}[/tex] [p and q are co-prime]

p=√5q …(1)

p²=5q [Squaring both the sides]

[tex]\frac{p²}{5}=q²[/tex]…(2)

p² divides 5, p also divides 5.

p=5m [m is any integer]

From equation 1,

√5q=5m

q=[tex]\frac{5m}{√5}[/tex]

q=√5m

q²=5m² [Squaring both the sides]

5 divides both p and q.

But p and q are co-primes.

It means our assumption is wrong.

√5 is irrational

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