Question

Give that √2 I irrational prove that (5+3√2)is an irrational number...



Please help!!!

Answer 1

It's so simple yaar

Put this (5+3root2)=a/b

Then take all the number and algebra to right side accept root2

Root2=a/b - 5 /3
=a-5b/3b

And u have prooved root 2 irrational so that relation we formed =root 2 and root 2 is irrational
So they are also irrational
Then u can reverse it after proving it irrational if required
............. As this the whole digit is proved irrational.... Hence proved

Answer 2

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,

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

⇒ $3 \sqrt{2}= \frac{p}{q} - 5$

⇒ $3 \sqrt{2} = \frac{p - 5q}{q}$

⇒ $\sqrt{2}= \frac{p-5q}{3q}$

We know that,

$\sqrt{2} \ is \ irrational\ (given)$

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

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.