Note that both radicals have an index number of 5, so we were able
to put their product together under one radical keeping the 5 as its index
number.

Since we cannot take the fifth root of and does not
have any factors we can take the fifth root of, this is as simplified as
it gets.

***Use the quotient rule of radicals to rewrite**

***Square root of 49 is 7**

Since we cannot take the square root of 5 and 5 does not have any factors
that we can take the square root of, this is as simplified as it gets.

Even though 40 is not a perfect cube, it does have a factor that we
can take the cube root of.

Check it out:

***Use the prod.
rule of radicals to rewrite**

***The cube root of 8 is 2**

In this example, we are using the product rule of radicals in reverse
to help us simplify the cube root of 40. When you simplify a radical,
you want to take out as much as possible. The factor of 40 that we
can take the cube root of is 8. We can write 40 as (8)(5) and then
use the product rule of radicals to separate the 2 numbers. We can
take the cube root of 8, which is 2, but we will have to leave the 5 under
the cube root.

Even though
is not a perfect square, it does have a factor that we can take the square
root of.

Check it out:

***Use the prod.
rule of radicals to rewrite**

***The square root of is **

In this example, we are using the product rule of radicals in reverse
to help us simplify the square root of .
When you simplify a radical, you want to take out as much as possible.

The factor of that we can take the square root of is . We can write as and
then use the product rule of radicals to separate the two numbers.
We can take the square root of which
is , but we will
have to leave the rest of it under the square root.

***Simplify fraction**

***Take the square root**

Note that both radicals have an index number of 2, so we are able to
put their quotient together under one radical keeping the 2 as its index
number. Since the radicand is a perfect square, we are able to take the
square root of the whole thing, which leaves us with nothing under the
radical sign.

Last revised on July 19, 2011 by Kim Seward.

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