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Prove that√5 is irrational

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Prove that√5 is irrational

Posted by Sradha Nanda Khadanga 5 years, 6 months ago

CBSE > Class 10 > Mathematics

3 answers

Yogita Ingle 5 years, 6 months ago

Let us consider that √5 is a “rational number”.

We were told that the rational numbers will be in the “form” of \frac {p}{q}form Where “p, q” are integers.

So, \sqrt { 5 } = \frac {p}{q}

p = \sqrt { 5 } \times q

we know that 'p' is a “rational number”. So 5 \times q should be normal as it is equal to p

But it did not happens with √5 because it is “not an integer”

Therefore, p ≠ √5q

This denies that √5 is an “irrational number”

So, our consideration is false and √5 is an “irrational number”.

Ankit Singh Thakur 5 years, 6 months ago

Let us assume√5 is irrational number. So, √5 is in the form of p/q where p and q are some Integers where q≠0. Since , We divide numerator and denominator by common factor to get a and b where a and b are co -prime. So , √5=a/b √5b = a Squaring both side, (√5b)^2 =a^2

Sradha Nanda Khadanga 5 years, 6 months ago

Prove that√5 is irrational

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