Question

prove that √5-7 is an irrational number​

Answer 1

Answer:

• let a and b are 2 co prime no and root 5 is irrational and root 5 - 7 is rational.
• root 5 - 7 = a/b
• root 5 = a/b + 7
• root 5 = (a + 7b) / b

Now (a + 7b) / b is a rational no as it is in p/q form where q not equal to 0. Hence root 5 can not be irrational so our assumption is wrong root 5 is rational and root 5 - 7 is irrational.

Hence proved