Question

Prove that 3√5-7is an irrrational no

Answer 1

Step-by-step explanation:

√5-7=p/q {where, p and q are integers having no common factors}. where , √5 and p+7q/3q are rational numbers. But this contradicts the fact that √5 is irrational. Therefore,3√5-7 is an irrational no

Answer 2

Answer:

Let us assume to the contrary that 3√5-7 is a rational no.

Such That ,

3√5-7=p/q {where, p and q are integers having no common factors}.

3√5=p/q+7

3√5=.p+7q/q

√5= p+7q/3q

where , √5 and p+7q/3q are rational numbers.

But this contradicts the fact that √5 is irrational.

Therefore,3√5-7 is an irrational no.