Hi,

The simplest way I can think of without using a calculator is to approximate values that make calculation easier.

For instance, consider if the values given were all the closest multiple of 10 to the given numbers, i.e. 20, 20 and 20. Now square these values and find their sum. It comes out to 1200. Now, take a look at the other value. The sum comes out to be 51, which can be approximated to 50 for simpler calculations. 50^2 2500, which is more than double of 1200. Clearly, the answer is (15+17+19)^2.

I think this is in fact faster than using the calculator itself. Of course, this is not a thumb-rule or a one-size-fits-all approach to solving this problem.

Hope this helps!