SOLUTION: radical 3 divided by radical 12

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Question 83391: radical 3 divided by radical 12
Found 2 solutions by josmiceli, bucky:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283%29+%2F+sqrt%2812%29
sqrt%283%2F12%29
sqrt%281%2F4%29
1%2F2
another way:
sqrt%283%29+%2F+sqrt%2812%29
sqrt%283%29+%2F+%28sqrt%284%29%2Asqrt%283%29%29
1+%2F+sqrt%284%29
1%2F2

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
sqrt%283%29%2Fsqrt%2812%29
.
Let's first work on the denominator. sqrt%2812%29 is equivalent to sqrt%284%2A3%29
.
Then applying the rule that sqrt%28a%2Ab%29+=+sqrt%28a%29%2Asqrt%28b%29 we can do another conversion to
see that:
.
sqrt%2812%29+=+sqrt%284%2A3%29+=+sqrt%284%29%2Asqrt%283%29
.
and for sqrt%284%29 we can substitute its equivalent 2 so that the next conversion
in the chain is shown on the right side of the expressions:
.
sqrt%2812%29+=+sqrt%284%2A3%29+=+sqrt%284%29%2Asqrt%283%29+=+2%2Asqrt%283%29
.
In the original given expression of the problem, we can now replace sqrt%2812%29
by its equivalent form 2%2Asqrt%283%29. That replacement results in the original given
form of the problem becoming:
.
sqrt%283%29%2Fsqrt%2812%29+=+sqrt%283%29%2F%282%2Asqrt%283%29%29
.
Note that sqrt%283%29 appears in as a factor in both the numerator and the denominator.
Therefore, it can be canceled and the result becomes:
.

.
So the simplified or reduced form of the original expression that was given is:
.
1%2F2
.
Hope this gets you a little more familiar with radicals and some of the methods you can
use to simplify expressions involving them.