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Prove that 3+2√5 is irrational number?

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Prove that 3+2√5 is irrational number?

Posted by Dilip Kumar Shah 5 years, 5 months ago

CBSE > Class 10 > Mathematics

3 answers

Helper . 5 years, 5 months ago

Jindagi bhar first chapter par atke rehna

Study Lover ?‍? ?‍? 5 years, 5 months ago

Let 3+2√5 be rational number. So,3+2√5=a/b(a and b are co-prime) A/q 3+2√5=a/b =>2√5=a/b-3 =>√5=(a-3b)/2b. a,b,3 and 2 are integers. So,(a-3b)/2b is rational. But,(a-3b)/2b=√5. (√5 is irrational). Hence, our assumption is wrong. So,3+2√5 is irrational... I hope this helps you.??

Yogita Ingle 5 years, 5 months ago

3 + 2√5 = a/ b
2√5 =a/b -3
√5 =a-3b/2b
√5 is rational.
This contradicta the fact that √5 is irrational.
So our supposition is incorrect.

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