Question

prove that 5 root 2 + 3 is an irrational number plz it's urgent​

Answer 1

Answer:

Here's your answer...

Step-by-step explanation:

Let us assume that 5 - 2 √3 is a rational number.

So, 5 - 2 √3 may be written as

5 - 2 √3 = p/q, where p and q are integers, having no common factor except 1 and q ≠ 0.

⇒ 5 - p/q = 2 √3

⇒ √3 = 5q - p/2q

Since, 5q - p/2q is a rational number as p and q are integers.

Therefore, √3 is also a rational number, which contradicts our assumption.

Thus, Our supposition is wrong.

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