Question

Show that 3 + √5 is irrational.​

Answer 1

Step-by-step explanation:

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Answer 2

$Let us assume number. \\ Now, \\ 3 + sqrt(5) = a/b numbers] sqrt(5) = [(a/b) - 3]; \\ sqrt(5) = [((a - 3b)/b)] Here, [((a - 3b)/b)] we know that sqrt(5) is an irrational so, [((a - 3b)/b)] ₁, \\ So, our assumption is wrong. 3 + sqrt(5) is an irrational number. \\ Hence, proved. is also a irrational number. \\ But number. that 3 + sqrt(5) is a rational \\ [Here a and b are co-prime is a rational number. O$

⇒ 3 + 5 = p q , where p and q are the integers and q ≠0. Since p , q and 3 are integers. So, p - 3 q q is a rational number.

Hence, is an irrational number.