Question

you have seen that √2 is not a rational number . show that 2√2 is not a rational number
please full solution​

Answer 1

Answer:

Therefore, r - 2 is also an irrational number. ⇒ r is an irrational number. Hence our assumption r is a rational number is wrong. Hence, 2 + √2 is not a rational number.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

by method of contradiction

let 2√2 be a rational number

then we can write 2√2 = p/q where q≠ 0

=> √2 = 1/2 [p/q]

=> √2 = [p/2q]

on RHS, p/2q is a rational number but on LHS √2 is an irrational number (given)

as LHS ≠ RHS, our assumption made at the beginning is wrong.

hence 2√2 is an irrational number