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Prove that 3+root 2 is a …

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Prove that 3+root 2 is a irrational number

Posted by Jahnavi Velagapudi 5 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Yangzee Sherpa 5 years, 1 month ago

Let us consider that 3√2 is a rational number. It can be written in the form p/q (p and q are co-primes). →p/q = 3√2. →p/3q = √2. Now, p/3q = integer/integer = rational number. But, this contradicts the fact that √2 is irrational. Therefore, our assumption that 3√2 is rational is WRONG. Hence, 3√2 is an irrational number. HoPe It HeLpS yOu??

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Gaurav Seth 5 years, 1 month ago

Let us consider that 3root2 is a rational number. It can be written in the form p/q (p and q are co primes)

p/q = 3root2

p/3q = root2

Now,

p/3q = integer/interger

= rational number

But, this contradicts the fact that root2 is irrational.

Therefore, our assumption that 3root2 is rational is WRONG.

Hence, 3root2 is an irrational number.

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CBSE > Class 10 > Mathematics