a property of mathematics says that square roots can be distributed over multiplication. that means...
TRANSCRIPT
126
3155
A property of mathematics says that square roots can be
distributed over multiplication.
That means a radical such as
135
can be written as
135
Or a radical expression such as
36can be written as
218
which simplifies to
6
Try these:
100520
1682
10
4
The property is often written:
abbaor
ab ba
A related property says that square roots are also
distributive over division:
ba
ba
ba
ba
or
2
502
50
Simplify:
25 5
3
273
27 9 3
Try one more:
75155 ?
Because 75 is not a perfect square . . .
75155
What makes this one different?
?
. . . we don’t know what its square root is.
We need to do something else to simplify it.
75
One possibility is to get an approximation
from a calculator
66.8
75
But another way to simplify it is to use what we just learned
about multiplying square roots.
325 325
35
75
What just happened?What allowed us to change
to
35 ?
One of our numbers
25was the square root of
a perfect square.
Since we know the square root of perfect squares,
325
we can write
as35
A radical term with all perfect square factors extracted from
the radical is said to be inSimplest Radical Form.
Look at this example:
Is it in simplest radical form?Have all perfect square factors been removed?
96 244 242
No—what is a perfect square factor of 24?
96 244 242
Did you say 4?We need to remove a factor of 4, so we will have:
96 242
You’re right!
642642 622 64
Just like when we simplify fractions,
when we simplify radicals, we are not through until all possible factors
have been removed.
And just like when we simplify fractions,
it saves a step or two if we remove the greatest possible
factor first.
Try this one:
31648 316
34
Try this one:
295185
295253 103
235
Try this one:
3
150 3
150 50
225 25