Math, asked by vishalpaswan45, 5 months ago

prove that 3+2√5 is irrtatonal​

Answers

Answered by booyah19
1

we know that root 5 is irrational so product of a rational number and irrational number is irrational number that is 2 root 5 is irrational number now 3 + 2 root 5 that is three plus in rational number but 3 is a rational number hence we conclude that the sum of a rational number and irrational number is always a irrational number hence it is prove that 3 + 2 root 5 is irrational number

Answered by amamaqazi
1

Step-by-step explanation:

Solving3 + 2√5 = a/b we get,

=>2√5 = a/b – 3

=>2√5 = (a-3b)/b

=>√5 = (a-3b)/2b

This shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.

so it contradictsour assumption.

Our assumption of3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number

Hence proved.

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