Algebra II : Factoring Radicals
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Example Questions
Example Question #4021 : Algebra Ii
Simplify
Cannot be simplified further.
To simplify a square root, factor out perfect squares:
Example Question #32 : Simplifying Radicals
Simplify 
While neither 512 or 
Remember the Product of a Power property of exponents can also apply to radicals, so:
Using this property, you get:
Both of these can be factored. Let's look at each term separately, and after we've factored them, we can recombine the terms at the end.
First look for a factor of 512 that is a perfect square. One factor of 512 is 256, which has a square root of 16, so:
Next look for a factor of 
Now combine these two terms:
Example Question #33 : Simplifying Radicals
Simplify 
While 24 is not a perfect square it does contain a factor that is a perfect square. Use the Power of a Product property to rewrite the problem:
24 contains the factors 4 and 6.
Example Question #34 : Simplifying Radicals
Simplify:
To simplify this radical, focus on each term separately. Recall that with square roots, for every pair of the same number or term, you can cross that under the radical and put one of them outside it. I'd recommend factoring 84 to its prime factors:
Therefore, you can take a 2 outside of the radical and leave 21 inside.
and
Put these all together to get your final answer of
Example Question #35 : Simplifying Radicals
Factor the radical:
The radical can be rewritten with common factors.
Pull out the factor of a known square.
The value of 
The answer is:
Example Question #36 : Simplifying Radicals
Simplify the radicals, if possible:
Simplify each term.
Multiply these terms together. Identical radicals multiplied by each other will cancel out the radical and leave the integer.
The answer is:
Example Question #37 : Simplifying Radicals
Simplify:
To add the radicals, first factor out the terms using known perfect squares.
Simplify the radicals with perfect squares.
Add the like terms.
The answer is:
Example Question #38 : Simplifying Radicals
Simplify:
To simplify this radical, I would look at each term separately. Remember that for every pair of the same term, cross the pair out under the radical and put one outside of the radical:
Now, put those all together to get your answer:
Example Question #4031 : Algebra Ii
Simplify, if possible:
Factor the square roots by common factors of perfect squares if possible.
The first term, 
Rewrite the terms.
The answer is:
Example Question #40 : Simplifying Radicals
Simplify:
This expression can either be split into common factors of perfect squares, or this can be multiplied as one term.
For the simplest method, we will multiply the two numbers in radical form to combine as one radical.
The square root of a number is another number multiplied by itself to achieve the number in the square root.
The answer is:
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