Question

show that 3+5√2is an irrational number ​

Answer 1

Answer:

Here is your answer:-

3+5√2

Let 3+5√2 be rational and have only common factor 1.

Let, 3+5√2 = a/b

5√2 = a - 3/ b

5√2 = a-3b/b

If a - 3b / b is rational so, 5√2 is also rational

but it is not possible .

It is contradiction to our assumption .

so, 3+5√2 is a irrational.

✨Hope it will help you.✨

Answer 2

Answer:

Here I'll not prove that _/2 is irrational. So taking this as granted, I'll solve this question.

_/2 = irrational

5 × _/2 = rational × irrational = irrational

3 + 5_/2 = rational + irrational = irrational

Therefore, 3+ 5_/2 is irrational.