Question

prove that 5 + 3 root 2 is an irrational number​

Answer 1

assumed.

let 5+3root 2 be rational

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

so here the equation is in rational.and so the root 2 .

but this contradicts the fact that root 2 is irrational.

this happened because of our wrong assumption.

therefore the 5+3root2 is irrational.

Answer 2

HI

here is ur answer

Step-by-step explanation:

let 5+3√2 be a rational number

in the form of a/b

5+3√2=a/b

3√2=a/b-5

3√2=a-5b/b

√2=a-5b/b

therefore a-5b/b is a rational number so √2 is also a rational number but this contradicts that our assumption is wrong therefore a-5b/b is a irrational number so √2 is also a irrational number

hence it is proved

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