Question

Show that 3+root 7 whole /5;;; is an irrational number

Answer 1

Answer:

Let given no is rational

so 3+√7/5=p/q

√7=5p/q-3

√7=5p-3q/q

hence 5p-3q/qis rational it's mean that √7is also rational, but we know that √7 is irrational this contradict our assumption that 3+√7/5 is rational , hence it is irrational

Answer 2

Answer:Here root is()

Let us assume to the contrary that 3+()7/5 is rational. So ,

3+()7/5 =a/b where a and b are co-prime and b/=0

Then,

3+()7/5=a/b

()7/5=a/b-3

()7/5=a-3/b (by lcm)

()7=a-3/5b

Since a and b are integers a-3/5b is rational.So even ()7 is rational. But this contradicts the fact that ()7 is irrational. This contradiction has arisen due to our incorrect assumption that 3+()7/5 is rational

Therefore, 3+()7/5 is irrational.

Step-by-step explanation: