Adding square roots

[nick3194]

Example:
sqrt(125) + sqrt(20) = sqrt(x). Find x.

[michel470]

[nick3194]

Thank you. Is there a trick to adding squares, or would it be easier to memorize them and just add.

[nsguy1350]

Depends on which squares you're adding. [unparseable or potentially dangerous latex formula] is treated differently than [unparseable or potentially dangerous latex formula], which is handled differently than [unparseable or potentially dangerous latex formula].

[nick3194]

Just two squares, not series or sequences.

[nsguy1350]

If one square is a multiple of another, then try to work with algebra to expand the expression. For example, [unparseable or potentially dangerous latex formula], which is easy.
If the outside digits sum to 10 and the second digit (from left to right, out of 4 digits. 12^2 + 34^2 has 1 as the first, 2 as the second, 3 as the third, and 4 as the fourth) is 1 greater than the third digit, sum the squares of the digits of the left number, then multiply the result by 101.
[unparseable or potentially dangerous latex formula].

[michel470]

I might add that if you are adding a square and its double(12^2 + 24^2), square the smaller one and multiply by five(I multiply by 5 sometimes by dividing the number by two and adding a zero when it's faster) 144*5= 144/2 * 10 = 720

In the event that you find yourself having to add squares that have no rhyme or rhythm(24^2 + 38^2) then you can do the one size fits all trick of adding squares: foil, multiply by two and add one

[nsguy1350]

[unparseable or potentially dangerous latex formula] follows the second trick :p
(2^2 + 4^2)x 101 = 2020.

[michel470]

True that! Ha didn't see that. Looking back on my tests though, it was actually 38^2 + 49^2, or more recently in a test I took, 61^2 + 62^2. If there are tricks for these, by all means, please make me aware, I'd really appreciate it. :)

[nsguy1350]

I don't know any tricks for those, but if you have your squares memorized, you could just crunch. 61^2 + 62^2 is 2(61)^2 + 2(61) + 1.