# Thread: Sum of Square Roots...

1. ## Sum of Square Roots...

Although 2^(1/2) + 3^(1/2) does not equal the square root of an integer, 27^(1/2) + 48^(1/2) does. Find every set of different positive integers p, q, and r all less than 100 such that p and q are not perfect squares and p^(1/2) + q^(1/2) = r^(1/2).

2. ## Re: Sum of Square Roots...

Originally Posted by thamathkid1729
Although 2^(1/2) + 3^(1/2) does not equal the square root of an integer, 27^(1/2) + 48^(1/2) does. Find every set of different positive integers p, q, and r all less than 100 such that p and q are not perfect squares and p^(1/2) + q^(1/2) = r^(1/2).
Here is a start but a solution without restrictions.
If $p=a^{2m+1}~\&~q=b^{2n}\cdot a$ where $\{a,b,m,n\}\subset \mathbb{Z}^+$ will work.
Now you must impose the restrictions.

3. ## Re: Sum of Square Roots...

wouldn't $p = c^{2n}a, q = b^{2n}a$ work as well?

4. ## Re: Sum of Square Roots...

Originally Posted by Deveno
wouldn't $p = c^{2n}a, q = b^{2n}a$ work as well?
Well of course it would.
I did say that was only a starting point.
We need to let the poster discover cases for him/her self.

5. ## Re: Sum of Square Roots...

oops, my bad...don't spank me, ok?