(58^2 + 58^2)/29^2 =

The question looks quite terrifying when you just look at the question stem, but once you check the answer alternatives, it is actually quite fun. With a little bit of simplification, you can make a strategic guess, since the alternatives are quite far apart.

First, let's simplify the expression a bit:

\(\frac{(58^2+58^2)}{28^2}=\frac{2*58^2}{28^2}=\frac{2*2^2*29^2}{2^2*2^2*7^2}=\frac{29^2}{2*7^2}\).

We can't simplify the equation further, so now we can start guessing. 29 is close to 30, so the numerator should be just short of \(30^2=900\). The denominator is 2 times 49, so just below 100. 900 over 100 is 9, so the result should be just short of that. Checking the answer choices, we see that B is 8, so that must be the answer.

If you are still not convinced, you can compare the numberator with \(25^2=625\). 625 over 100 would be 6.25 and since 29 is closer to 30 than to 25, the precise result should be somewhere between 6.25 and 9, however closer to 9 than to 6.25.