Question

prove that √5 is irrational
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Answer 1

$\huge\bigstar\underline\pink{Answer:-}$

$\huge\bold{To Prove:-}$√5 is an

irrational number .

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$\huge\bold\purple{prove:-}$

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Let, √5 is an rational number.

so, $\bf{√5 = p / q}$ [ where p and q are co- primes and q not equals to zero]

squaring on both sides,

so, (√5)² =( p / q)²

↪️ 5 = p²/q²

↪️ 5q² = p²

☯ 5 is divided by p²

☯ 5 is divided by p

. ° . 5 is a factor of p.

Let , 5m = p

☯ 5q² = 5m

so ,

↪️ 5q² = (5m)²

↪️ 5q² = 25m²

↪️ q² = 5m ²

. ° . 5 is divided by q²

5 is divided by q²

. ° . 5 is a common factor of p and q

But , p and q are co - primes .

. ° . Our Assumption is Wrong .

. ° . √5 Is an Irrational number .