SOLUTION: I do not know how to do this problem, so your help is greatly appreciated!
4. Perform the indicated operations:
4√[18] + 2√[32] –√[8]
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Question 85158: I do not know how to do this problem, so your help is greatly appreciated!
4. Perform the indicated operations:
4√[18] + 2√[32] –√[8]
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
.
To simplify expressions such as this think in terms of factoring the quantities under the
radicals. Especially look for factors that are perfect squares because they can be taken outside
the radicals.
.
Let's operate on one term at a time beginning with . The 18 can be factored into
which makes the term become . This in turn can be split into two
radicals: . But so the sequence of simplification
becomes:
.
.
Then putting the original factor of 4 back in front of the radical, you get:
.
.
Substitute this simplification for the first term in the original problem and you get:
.
.
On to the second term in the problem. Use the same method on .
Factor it
to get:
.
.
Then from the second term, don't forget the 2 that originally multiplied the radical. So
the entire term from the original equation becomes .
Substitute this into the problem equation that already contains the simplified first term
and the reduced form is now:
.
.
And now to the last term to be simplified:
.
.
This term had no multiplier in the original expression, so substituting it back into the
version with the two terms already simplified results in:
.
.
Now notice that all three terms contain as a factor. Factoring it out results
in the distributed multiplication:
.
.
and the terms in the parentheses combine to give the final answer of:
.
.
Hope this helps you to understand a method to follow in simplifying radical expressions
of this sort.
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