Algebra II : Factoring Radicals
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #41 : Simplifying Radicals
Factor:
Rewrite the first term using a factor of a perfect square.
Combine like-terms.
The answer is:
Example Question #42 : Simplifying Radicals
Simplify:
Break up the radical that can be simplified.
Rewrite the expression.
A radical multiplied by itself will eliminate the radical and leave just the integer.
The answer is:
Example Question #41 : Simplifying Radicals
Simplify:
Evaluate by rewriting both radicals by factors of perfect squares.
The radicals 
Simplify this radical.
Replace the term.
The answer is:
Example Question #43 : Simplifying Radicals
Factor:
Simplify each radical using values of perfect squares as factors.
Replace the terms into the original expression and simplify.
The answer is:
Example Question #41 : Simplifying Radicals
Factor:
Multiply all the terms in the radical to combine as one radical.
Rewrite the radical using known perfect squares as factors.
Simplify the known radicals.
The answer is:
Example Question #41 : Simplifying Radicals
Simplify the expression.
The best way to approach this problem is to try to pull out perfect squares. In this case the x squared term can be separated from the 80. The 80 can then be broken down into 16, a perfect square, and 5.
Simplify the x squared and root 16 terms.
Example Question #41 : Factoring Radicals
Simplify the following radical by factoring:
The goal of simplifying a radical by factoring is to find a factor of the radicand that has a neat whole number as a square root. If this factor is difficult to determine simply by looking at the radicand, a good way to start is by factoring the radicand until you notice a factor that has a whole number as a square root, and can therefore be taken out of the radical. Assuming we couldn't identify a factor of 150 with a neat square root, we could start the factoring by taking out the smallest factor possible, which for even numbers would be 2:
Neither number has a neat square root, so we'll continue by factoring out the next smallest factor of 3 from 75:
At this point we can see that one of our factors, 25, has a neat square root of 5, which we can take out from under the radical, and now that none of the factors left under the radical can be simplified any further, we simply multiply them back together to give us the most simplified form of our radical:
Example Question #1372 : Mathematical Relationships And Basic Graphs
Simplify:
To simplify this expression, I'd recommend factoring it down to its prime factors: 
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