Question

Prove that 2+3√5 irrational Number​

Answer 1

Answer:

2+ root 3/5 is irrational number.

Step-by-step explanation:

solution :

to prove 2 + root 3 / 5 is irrational , let us assume that 2 + root 3 / 5 is rational number .

2+root 3/5 = a/b; b not equal to 0 and a & b are integers.

= 2b+root 3 = 5

= root 3 = 5b-2b

= root 3 = 5a-2b/b

since a and b are integers, so 5a - 2b will also be an integer .

so 5a-2b/b will be rational .

which means root 3 is also rational .

but we know root 3 is irrational number. (given)

Thus, a contradiction has risen because of incorrect assumptions.

Thus, 2+root 3/5 is irrational number.