Question

prove that 7-2root3 is an irrational number​

Answer 1

Answer:

Since root 3 is irrational the whole expression becomes irrational.

Step-by-step explanation:

ln short as above because we save time for other answers.

Answer 2

Proof :

We proof the problem by contradiction.

Without losing generosity, we consider that (7 - 2√3) is a rational number.

Then, 7 - 2√3 = a/b, where both a and b are integers with b ≠ 0

⇒ 2√3 = 7 - a/b

⇒ 2√3 = (7b - a)/b

⇒ √3 = (7b - a)/(2b)

Since a, b are integers, both (7b - a) and 2b are integers, and this implies that √3 is a rational number, which is a contradiction.

∴ (7 - 2√3) is an irrational number.

Hence, proved.