SOLUTION: Please help me by showing me how to do this problem and give me some tips on how to solve other problems like this : 1) If n^2˃4 and n is a natural number, then n ˃2 Tha

Algebra ->  Proofs -> SOLUTION: Please help me by showing me how to do this problem and give me some tips on how to solve other problems like this : 1) If n^2˃4 and n is a natural number, then n ˃2 Tha      Log On


   

Question 953371: Please help me by showing me how to do this problem and give me some tips on how to solve other problems like this : 1) If n^2˃4 and n is a natural number, then n ˃2
Thank you very much
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
start with n^2 > 4.

take the square root of both sides of the equation.

you will get n > plus plus or minus sqrt(4) which becomes.

n > plus or minus 2.

since n is a natural number, it can't be negative, and you are left with:

n > 2.

taking the square root of both sides of an inequality preserves the inequaltiy.

for example:

assume that 5^2 > 24

this is true since 25 is greater than 24.

no argument there i hope.

take the square root of both sides of this equation to get:

sqrt(25) > sqrt(24)

you will get 5 > 4.898979486...

you took the square root of both sides of the inequality and the inequality was preserved.

the left side was greater at the beginning and at the end of the square root of both sides of the inequality operation.