Question

Prove that 3t2√5 is irrational
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Answer 1

Answer:

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.

Our assumption of3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number

Hence proved

Answer 2

Answer:

Let. 3t2√5 be a rational number

So it can be represented in the firm p/q where p and are at the lowest form.

Therefore, 3t2√5=p/q

=6t√5=p/q

=√5=p/q6t

Since p,q,6and t are all integers and are rational hence,√5 is also rational.

But we know that √5 is irrational and it cannot be rational.

Therefore 3t2√5 is rational