Question

prove that 2+3root2 is irrational

Answer 1

Answer:

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Answer 2

2 + 3√2 is irrational number

__________ [TO PROVE]

Let us assume that, 2 + 3√2 is a rational number

=> 2 + 3√2 = $\dfrac{a}{b}$

Here, a and b are co-prime numbers.

=> 3√2 = $\dfrac{a}{b}$ - 2

=> 3√2 = $\dfrac{a\:-\:2b}{b}$

=> √2 = $\dfrac{a\:-\:2b}{3b}$

Here..

$\dfrac{a\:-\:3b}{3b}$

is rational number.

So, √2 is also a rational number.

But we know that √2 is irrational number.

So, our assumption is wrong.

2 + 3√2 is irrational number.

___________ [HENCE PROVED]

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