Question

show that root 13 is an irrational number​

Answer 1

Answer: The rational root theorem guarantees its roots aren't rational and since √13 is a root of the polynomial, it is irrational. Let √p=mn where m,n∈N. and m and n have no factors in common. So mn can not exist and the square root of any prime is irrational.

Step-by-step explanation:

Answer 2

Answer:

√13=p/q,where p,q belongs to integers ,qis not equal to zero

q√13=p

squaring on both sides

(q√13)²= p²

13q²=p²

here 13 divides p²

p=13k

13q²=( 13k)²

13q²= 169k²

q²= 169k²/13

q²= 13k²

here 13 divides q²

q²=13k² is a rational number

√13 is a rational number

our assumption √13is rational number is wrong

therefore √13 is a irrational number