1.

Given that root two is irrational prove that (5+3root two)is an irrational

Answer» HEY friend, Harish here.

Here is your answer:

Given that,

√2 is an irrational number.

To  prove,

5 + 3√2 is an irrational number.

Assumption:

Let 5 + 3√2 be a RATIONAL  number.

Proof:

As 5 + 3√2 is assumed to be rational , then it MUST be of the form p/q, Where q≠0.

Then,

5+3 \sqrt{2} = \frac{p}{q}

3 \sqrt{2} = \frac{p}{q}-5 = \frac{p-5q}{q}⇒ 

\sqrt{2}= \frac{p-5q}{3q}⇒ 

We know that,

\sqrt{2}\ is \ irrational\ (Given)

\frac{p-5q}{3q} \ is \ rational

As rational ≠ irrational.

We contradict the statement that 5+3√2 is rational.

Therefore it is irrational.
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Hope my answer is helpful to you.


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