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Prove that 5-root3 is irrational

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Prove that 5-root3 is irrational

Posted by Ranganathan V 4 years, 5 months ago

CBSE > Class 10 > Mathematics

4 answers

Kyira Singh 4 years, 5 months ago

If possible root 5 is rational no. 5=p/q( where q not equal 0 ,, p/q having no factors other than 1) Squaring both sides 5=P2/q2 P2=5q2....1 P2 is divisible by5 P is also divisible by 5 Putting p=5 in 1 (5m)2=5q2 25m2=5q2 5m2 =q2 q2 is divisible by 5 q is also divisible by 5 5 is common factors of p and q This is contradiction So,our assumption is wrong Root 5 is irrational no.

Rohit Singh 4 years, 5 months ago

Let us assume the given number be rational and we will write the given number in p/q form ⇒5− 3 = q p ⇒ 3 = q 5q−p We observe that LHS is irrational and RHS is rational, which is not possible. This is contradiction. Hence our assumption that given number is rational is false ⇒5− 3 is irrational

Akshit Kaktwan 4 years, 5 months ago

I know anwer but can't type sorry

Shyam Singh Bangari 4 years, 5 months ago

soory

ANSWER

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