Title: Multiplying
1Multiplying
and Dividing
Radicals
2A property of mathematics says that square roots
can be distributed over multiplication.
That means a radical such as
can be written as
3Or a radical expression such as
can be written as
which simplifies to
4Try these
5The property is often written
or
6A related property says that square
roots are also distributive over division
7or
8Simplify
9Try one more
10Because 75 is not a perfect square . . .
What makes this one different?
. . . we dont know what its square root is.
We need to do something else to simplify it.
11One possibility is to get an approximation
from a calculator
12But another way to simplify it is to use what
we just learned about multiplying square roots.
13What just happened?
What allowed us to change
to
?
14One of our numbers
was the square root of a perfect
square.
15Since we know the square root of perfect squares,
we can write
as
16A radical term with all perfect square factors
extracted from the radical is said to be in
Simplest Radical Form.
17Look at this example
Is it in simplest radical form?
Have all perfect square factors been removed?
18Nowhat is a perfect square factor of 24?
19Did you say 4?
We need to remove a factor of 4, so we will have
Youre right!
20Just like when we simplify fractions,
when we simplify radicals, we are not
through until all possible factors
have been removed.
21And just like when we simplify fractions,
it saves a step or two if we remove the greatest
possible factor first.
22Try this one
23Try this one
24Try this one