Question

show that 5+2√3 is an irrational number ​

Answer 1

Answer:

• Given - 5 + 2 root 3

• To prove - it is an irrational no.

• Solution -

Let suppose it is a rational no.

5 + 2 root 3 = p/q where p and q are co primes

2 root 3 = p /q - 5

2 root 3 = p - 5 / 5q

2 root 3 = p - 5 / 5q

P - 5 /5 q is a rational no. and 2 root 3 is an irrational no.

Rational is not equal to irrational

Our assumption is wrong.

5 + 2 root 3 is an irrational number.

Hence , proved.

Answer 2

Answer Expert Verified
5 - 2 √3 = p/q, where p and q are integers, having no common factor except 1 and q ≠ 0. ... Therefore, √3 is also a rational number, which contradicts our assumption. Thus, Our supposition is wrong. Hence, 5 - 2 √3 is an irrational number.