PA_M6_S1_T1_Square Root Notation Transcript
Because I always have two roots for a square root, a positive and
negative, there is a special notation that I can use to specifically
request one or the other of the square roots of a number. This notation
is generically called radical notation. I'm going to talk about square
root notation in particular right now.
In square root notation, my number, that I'm trying to find the square
root for, is located under
this little radical sign,
and that's what it's
called, this little check
mark box is called a
radical. The number that
I'm putting inside, this is
the value I want the square
root for, is called the
radicand and when I put it
under there without an
explicit sign in front of
it, I am looking for the
positive square root of my
radicand. The positive
square root is also known
as the principal square root, and we typically use it whenever we are
taking the square root of perfect squares.
If I want something other than that, I will
go out and place a negative sign in front
of the radical sign. In that case I will be
looking for the negative square root of a,
and notice that I have expressly put that
negative sign in.
So let's practice a little bit with some
examples.
Here is √
in radical notation. There is no negative sign in front. I
am looking for the positive√
. 121 is the product of 11 * 11 so that 11
is my square root, and in this case it's the only one I give because I've
expressly ask for only the positive root.
In the next example,
is -25.
√
√
, 625 can be expressed as 25 * 25, so that my
The square root of 0 is still 0. It's neither negative nor positive. It's
just 0.
is asking for the number that when multiplied by itself will give me
√
-36, but because squaring will also square the negative sign, there's no
way to get a real root out of this, so there is no real square root for -
36. On the other hand if I put the negative sign in front and I'm looking
for √ , I'm looking for the negative of the number that when squared
gives me a 36. 36 is 62, so my √
is -6.
These are some quick examples of working with radical notation for square
roots of numbers.