When you're breaking down the square root in the quadratic formula into several parts- say it was the originally the square root of 80 so you break it down to square root of 4 and square root of 20-would the results be added or multiplyed? Because I know when you further break this down you get 2, the square root of five and the square root of four. Would you add the two 2's, or multiply them? And is there a +/- sign in front of each coefficient or is it just in front of the ACTUAL square root, not the broken down parts of the square root? Thank you so much for clarifying this!

Question

When you're breaking down the square root in the quadratic formula into several parts- say it was the originally the square root of 80 so you break it down to square root of 4 and square root of 20-would the results be added or multiplyed? Because I know when you further break this down you get 2, the square root of five and the square root of four.  Would you add the two 2's, or multiply them? And is there a +/- sign in front of each coefficient or is it just in front of the ACTUAL square root, not the broken down parts of the square root? Thank you so much for clarifying this!

Reiny · Answer

You probably have a something like this
(? ± √80)/??

so when you "break down" the √80 you would look for the largest perfect square which divides into 80. That would be 16

so √80 = √16 x √5
= 4√5 , which means 4 times the square root of 5
when you put that back into the formula expression you would of course keep the ±

get used to checking your work with a calculator.
find √80 and note its decimal answer
now find √5 , then multiply that by 4
You should get the same answer correct to about 8 decimal places, if not, you made a mistake.