Multiplying

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