Question

Prove that 3+2√5 is irrational.​

Answer 1

Answer:

answer for your question

Answer 2

Answer:

Prove 3+2√5 is irrational.

→ let take that 3+2√5 is rational number

→ so, we can write this answer as

⇒3+2√5 = a/b

Here a & b use two coprime number and b

is not equal to 0

, => √5 = (p/q) -3

=> √5 = (p-3q)/q

Here, in RHS , numerator is the difference of 2 integers, which always remains an integer. & denominator is also an integer, not = 0.

=> RHS is a rational number ( as, all the conditions for being a rational number, have been satisfied )

But LHS is an irrational number. ( by theorem, √5 is an irrational number)

=> LHS not = RHS

=> our assumption (that 3+√5 is a rational number) is wrong.

Hence, 3+√5 is an irrational number

Step-by-step explanation:

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