Question

Prove that (3+2 root 5)^2 is irrational number.

Answer 1

Answer:

Given:3 + 2√5

To prove:3 + 2√5 is an irrational number.

Proof:

Letus assume that 3 + 2√5 is a rational number.

Soit can be written in the form a/b

3 + 2√5 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving3 + 2√5 = a/b we get,

=>2√5 = a/b – 3

=>2√5 = (a-3b)/b

=>√5 = (a-3b)/2b

This shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.

so it contradictsour assumption.

$\blue{Our assumption of3 + 2√5 is a rational number is incorrect.}Ourassumptionof3+2√5isarationalnumberisincorrect.$

3 + 2√5 is an irrational number

$\red{Hence. proved}$

Answer 2

Answer:

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