Question

prove that 6- 5 root 2 is irrational

Answer 1

Hey friend✋! here is your answer

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◆To prove--- 6-5√2 is irrational

✅Proof- let assume 6-5√2 is rational
so,

✔️6-5√2=a/b { where a & b are co-prime }

✔️-5√2=a/b-6

✔️Take LCM on RHS
✅-5√2=a-6/b

✔️-√2=a-6/5b

◆Here -√2 & a-6/5b are two rational number but the fact is -√2 is irrational number.

✅This contradiction arises due to our wrong assumption. So 6-5√2 is irrational

______Hence proved_________

⭐️Hope it helps you⭐️