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Prove root7+root5 is an irrational

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Prove root7+root5 is an irrational

Posted by Aviansh Kumar 7 years, 10 months ago

CBSE > Class 10 > Mathematics

4 answers

Shivam .G 7 years, 10 months ago

first assume that it is rationalise in the form of p/q where p and q are co prime nos.

root 5+rot7=p/q

whole square both side...

12+2root35=(p/q)whole sqare

therefore root 35=(p square-12q square)/q square

lhs= irrational no.

rhs=rational no.

this contradicts our assumption that root5+root7 is rational..

therefore it is irrational no.

Mini Sharma 7 years, 10 months ago

Let √7+√5 be rational and its simplest form be a/b where a and b are co primes. Then √7+√5=a/b Squaring on both sides 12+2√35=a square/b square 2√35=a square /b square -12 √35=a square -12b square/2b square Since the number on the rhs is a non zero integer Therefore it is a rational number Then √35 is also a rational number But this contradicts the fact that √35 is an irrational number Therefore our supposition is wrong Hence √7+√5 is an irrational number

Pranzil Sihal 7 years, 10 months ago

This*

Pranzil Sihal 7 years, 10 months ago

Thai is an ncert ques see in ncert question

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