Question

given that √2is irrational,prove that (5+3√2) is an irrational no.

Answer 1

Hey friend !

Here's your answer :

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Let us assume in contradiction that 5+3√2. is rational number

Let 5+3√2 be a/b where a and b are co-primes.

5+3√2 = a/b

√2 = a/b - 5/3

√2 = 3a - 5b / 3b

√2 = integer / integer { p / q form }

We know that if a number is in the form of p/ q then it is an rational number .

But given that √2 is irrational .

So , our assumption is wrong

5+3√2 is irrational number.

# Hope it helps #