Question

Show that 3+5under root 2 is irrational no

Answer 1

Answer:

your answer is in attachment..

Answer 2

Answer:

No answer. Just check out the explanation.

Step-by-step explanation:

We know that √2 is irrational.

We have to prove that 3 + 5√2 is irrational.

We'll do this by the contradiction method.

Let 3 + 5√2 be a rational number.

Then, there exists p and q such that 3 + 5√2 = p/q, where p and q are integers, q ≠ 0 and p and q are co-primes, ie, they have no other factor other than 1 in common.

3 + 5√2 = p/q

5√2 = p/q  - 3

5√2 = (p-3q)/q

√2 = (p-3q)÷(5q)

RHS represents a rational no. because if we do any operation out of +, -, ×, and ÷ to a rational no, it remains a rational no.

However, LHS represents an irrational no.

Thus, our supposition is wrong.

Hence, 3 + 5√2 is irrational.