Question

Prove that 3+5√2 is irrational.​

Answer 1

Step-by-step explanation:

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

So it can be written in the form a/b

3 + 5√2= a/b

Here a and b are coprime numbers and b ≠ 0

Solving 3 + 5√2 = a/b we get,

=>5√2 = a/b – 3

=>5√2= (a-3b)/b

=>√2 = (a-3b)/5b

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

so it contradictsour assumption.

Our assumption of 3 + 5√2 is a rational number is incorrect.

3 + 5√2 is an irrational number

Hence proved

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Answer 2

Step-by-step explanation:

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