Question

Prove that2+5 root 3 is an irrational number, given that root 3 is an irrational number

Answer 1

Answer:

assume that 2+5√3 is a rational number. Therefore, a-2b/5b is in the form of a/b which is rational number. ... Therefore, our assumption is wrong and 2+5√3 is an irrational number.

Answer 2

Answer:

Step-by-step explanation:

2+5√3 we assume that it is rational number

p and q are coprimes.q ≠ 0.

now,

⇒2+5√3=p/q

⇒5√3=p/q-2

⇒(5√3)=(p/q-2)

⇒5√3=p-2q/q

⇒√3=p-2q/5q

√3 is an irrational number.  SO L.H.S IS AN IRRATIONAL .  BUT R.H.S IS AN RATIONAL

IRRATIONAL NO. ≠RATIONAL NO. ,OUR ASSUMPTION IS WRONG.IT IS AN IRRATIONAL NUMBER