SOLUTION: Simplify the radical expression. Assume all variables represent positive real numbers. square root 12a^3/25

Question 77185: Simplify the radical expression. Assume all variables represent positive real numbers.
square root 12a^3/25
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
The problem asks you to simplify this expression. To do this you need to get as many factors
out from under the radical sign as possible.
.
Let's start by factoring each term under the radical. Look for factors that are squares.
.
For example ... 12 can be factored a number of ways: (12 and 1), (6 and 2), (4 and 3). The
best set of factors for us is 4 and 2 because 4 is a square.
.
can be factored into
.
Making these substitutions results in the expression becoming:
.

.
and this can be expanded to:
.

.
Next take the square root of all the squares. When you do that the expression becomes:
.

.
and by collecting the terms that are now out from under the radical sign we get:
.

.
and the two terms with radicals can be combined under one radical to get the answer in
the form
.

.
Hope this gives you an insight into some of the processes that can be used to simplify
problems containing radicals.

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