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Prove that√5 is irrational.

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Prove that√5 is irrational.

Posted by Aditya Jha 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sukhman Singh Bhullar 4 months ago

Let √5=a/b is a rational number Where a and b are co-prime Squaring both sides (5)²=a²/b² 5=a²/b² b²=a²/5 -(1) .'. a² is divisible by 5, also a is divisible by 5 Let a/5=c a=5c Put this value of a in (1) b²=(5c)²/5 b²=25c²/5 b²=5c² c²=b²/5 b² is divisible by 5 also b is divisible by 5 .'. This is a contradication that √5 is a rational number .'.√5 is an irrational number

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