Video Transcript
Solve 𝑥 squared equals two
hundred, leaving your answer in surd format in its simplest form. So it says surd format here. That might say in radical format
or it might say expressing it as a multiple of irrational number; you could
encounter that in either of those forms. So let’s just write that
expression out: 𝑥 squared equals two hundred. Well if we’re solving that, we
want to know what 𝑥 equals. So what we have to do to 𝑥
squared to turn it into 𝑥? Well, we’ve got to take the square
root of both sides of the equation. So the square root of 𝑥 squared
is 𝑥 and that’s equal to the square root of two hundred. But it’s not quite as simple as
that because it could be positive root two hundred or it could be negative root two
hundred because negatives times negatives make positives.
So there we are, 𝑥 is equal to
plus or minus root two hundred. Well we’ve solved it, and but we
still need to put it into its simplest form. So we’ve got to try to look for
factors of two hundred, which are square numbers and we want the biggest one of
those that we can. So I’m looking for the largest
square factor that I can find of two hundred and then times something else. So two hundred, so we’re gonna
divide by two, divide by three, divide by four until we find the other factor which
is a square number. So two hundred divided by two is a
hundred. Ah, that is a square number. So it’s a hundred times two. And we can split the hundred and
the two out remember, so that’s plus or minus the square root of a hundred times the
square root of two. And because the square root of a
hundred is ten. That becomes ten times root two or
ten root two. So our final answer here is plus
or minus ten root two.
