Hello friends my name is Kevin and I'm coming to you from Magoosh, and today we're looking at a fundamental
math property. Something that students tend to confuse and make a mistake with so that's
where we're starting with with the mistake. As you can see the question is what's the
error and I wrote this problem on the board and some student solved the problem they thought that
they got it right but they got it wrong actually. So the question says solve this equation for y
so the equation is 10 y squared minus 10 x squared equals 250. So first they're dividing by 10 on
either side which is good to simplify the problem. So then they end up with y squared minus x squared
equals 25 then they add x squared to both sides to eliminate um and get y by itself on one side.
Then they get y squared equals x squared plus 25 and they take the square root of all of it
to end up with y equals x plus 5. Do you think you see the mistake? Did you see it? Is it up here?
No, it's down here. This is the big mistake, no no no don't do this!
They are confusing the distributive property
of multiplication and division with addition and subtraction. So the rule is you cannot
cannot do square root of p plus q. Cannot do this!
You just can't break it apart and take the square root of each individual item there and that's what
they did here. Really what they were thinking was like oh x squared well I take the square root of
that and I get x and if I take the square root of 25 I get 5. So they're thinking oh I'll just take
x squared and 25 if I can write it properly let's write it better
25 and then I get my answer. But you can't do that. It's just not the rule, it does work however
if you have p times q and put that under square root. Then you can take the square root of each
item that is there and there's a really good way to remember this, if we think about the
pythagorean theorem. Pythagorean theorem is a squared plus b squared equals c squared. Now Mr.
Pythagoras was not a cruel and evil person who wanted to make things more difficult for us. It
wasn't like he decided to make it a squared plus b squared equals c squared and it could actually be
a plus b equals c. They're not the same thing, you can't take the square root of this side to get a
plus b that's just not how it works. So always think about the pythagorean theorem you can't
simplify this to a plus b equals c if we could we probably would. You know math can be difficult
enough we try to simplify as much as possible but in this case uh Mr. Pythagoreas has given
us the easiest version. So remember that when you're adding or subtracting excuse me adding
or subtracting you cannot take the square root of both of the items that are there. All right so
that is our math foundation rule for the day. We'll put a link below the video so that you can go and
read more about this math fact. Be excellent to the universe and I'll see you next week!