Question

show that √5+√7 whole square is irrational


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Answer 1

Answer:

Step-by-step explanation:

Here can solve this by using the formula (a+b)2 = a2+2ab+b2

Let (root 3 + root 5)2 be of the form a/b where a and b are co-primes and b is not equal to zero.  

(root 3 + root 5)2 = a/b

3 + 2 (root 3) (root 5) + 5= a/b

8 + 2 (root 3) (root 5) = a/b

2 (root 3) (root 5)= a/b-8

2 (root 3) (root 5)= 8b-a/b

2 (root 15) = 8b-a/b

root 15 = 8b-a/2b

Here the RHS is rational while the LHS is irrational.

This is not possible and therefore contradicts our assumption that (root 3 + root 5)2 is rational.  

Therefore (root 3 + root 5)2 is irrational