Question

prove that √3.2-3√5 is an irrational number

Answer 1

assume that root 3.2 -3root 5 be a rational no.
=>root 3.2 -3 root 5=a/b ( where a n b are co prime no. and some integers)
root 3.2= a/b+3 root 5,
by taking lcm we get,
root 3.2 =a+3 root 5 by b
since a n b are integers
so a+3 root 5 , b are also integers
but it contradict our assumptions that root 3.2 - 3root 5 is a rational no.
so hence proved

Answer 2

Answer: Is a Rational Number

Step-by-step explanation:

assume that root 3.2 -3root 5 be a rational no.

=>root 3.2 -3 root 5=a/b ( where a n b are co prime no. and some integers)

root 3.2= a/b+3 root 5,

by taking lcm we get,

root 3.2 =a+3 root 5 by b

since a n b are integers

so a+3 root 5 , b are also integers

but it contradict our assumptions that root 3.2 - 3root 5 is a rational no.

so hence proved