Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

1. Prove that if a positive integer is of the form 6q+5 then it is of the form 3q+2 for some integer q but not conversely.

2. Prove that root p + root q is irrational where p and q are primes. Please answer it with correct and appropriate proofs..... i need it complete... Hope someone will help this helpless person.... Thankzzzz.....

Let a be any positive integer and b = 6 so using euclids algorithm a = 6q + r for some integer q ≥ 0 where r = 0,1,2,3,4,5 so r lie from 0≤r≤6 so a = 6q , a=6q+1 , a=6q+2 , a=6q +3 , a=6q+4,a=6q+5,a=6q+5 we can say 6q+1 = 2 so 3q +1 = 2k1 + 1 which is positive integer (6q +3)=(6q+2)+1=2(3q+1)+1 = 2k2+1 where k2 is an integer (6q+5)=(6q+4) +1 =2(3q+2)+1=2k3 +1 where k is an integer so we can say that 6q+1 ,6q+3 ,6q+5 are integers so 6q+1,6q+3,6q+5 are not exactly divisible by 2 u may know that these expression is used for the odd numbers or therefore any odd integer can be expressed by n+1 ,n+2 ,n+3 where n = 6q so hence prove i hope u are agree with my ans

Let a be any positive integer and b = 6 so using euclids algorithm a = 6q + r for some integer q ≥ 0 where r = 0,1,2,3,4,5 so r lie from 0≤r≤6 so a = 6q , a=6q+1 , a=6q+2 , a=6q +3 , a=6q+4,a=6q+5,a=6q+5 we can say 6q+1 = 2 so 3q +1 = 2k1 + 1 which is positive integer (6q +3)=(6q+2)+1=2(3q+1)+1 = 2k2+1 where k2 is an integer (6q+5)=(6q+4) +1 =2(3q+2)+1=2k3 +1 where k is an integer so we can say that 6q+1 ,6q+3 ,6q+5 are integers so 6q+1,6q+3,6q+5 are not exactly divisible by 2 u may know that these expression is used for the odd numbers or therefore any odd integer can be expressed by n+1 ,n+2 ,n+3 where n = 6q