Question

prove that 5+√2 is irrartiona and 3+5√3 is irrational no. pls help and i dont want any
c hut iya answer class 10 ka hai​

Answer 1

Hey friend, Harish here.

Here is your answer:

Given that,

√2 is irrational

To prove:

5 + 3√2 is irrational

Assumption:

Let us assume 5 + 3√2 is rational.

Proof:

As 5 + 3√2 is rational. (Assumed) They must be in the form of p/q where q≠0, and  p & q are co prime.

Then,

⇒

⇒ 

⇒ 

We know that,

And, Rational ≠ Irrational.

Therefore we contradict the statement that, 5+3√2 is rational.

Hence proved that 5 + 3√2 is irrational.

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Hope my answer is helpful to you.

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