Question

Prove that 2+3 root 5 is an irrational number

Answer 1

so, assume that 2+3root 5 is rational.
2+3root5=p/q,where p and q are coprimes and q not equals to 0.
3root 5=p/q-2.
root 5=p/q-2/3.
A rational number never equals to an irrational number.
We assume that p and q are coprimes and q not equals to 0.
so, our assumption is wrong.
2+3root 5 is an irrational number.
Thank you, hope it helps.....

Answer 2

Answer:

2+3√5 = p/q, where p and q are co primes and q not equals to 0.

Step-by-step explanation:

Let x = 2 + 3√5  be a rational no.

x - 2 = 3√5

x - 2 / 3 = √5

Since x is rational, x-2 is rational and hence x-2 / 3 is also a rational no.

⇒ √5 is a rational no. , which is a contradiction.

Hence 2 + 3√5  must be an irrational number

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