First, it's important to know that 1. Odd + odd = even ex. 1+1=2 2. 2 times any counting number is equal to even ex. 1 x 2 = 2 3. Even + odd = odd ex. 2+1=3 Then we can say that m^2 is odd because if it is added to 1, the result is even (as shown in number 1) And because m^2 is odd, then m is odd because it sqaure root will not result to even when the square is odd. Therefore we can say that 2n+m is odd because 2n is even (example #2) and adding odd to that will result in an odd number (#3 example).

This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
2n + m is odd because in m^2 + 1, it is said to be even so if you remove the one, the resulting term which is m^2 will be odd so as its square root m. That means, m is odd and if it is added to 2n which is even because any number multiplied by 2 willl be eventhen 2n + m is odd becausea number + odd yields odd.