Algebra II : Non-Square Radicals

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Non Square Radicals

Possible Answers:

Correct answer:

Explanation:

To solve this, remember that when multiplying variables, exponents are added.  When raising a power to a power, exponents are multiplied.  Thus:

Example Question #2 : Non Square Radicals

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Since , we can multiply 18 by  to yield the lowest possible perfect cube:

Therefore, to rationalize the denominator, we multiply both nuerator and denominator by  as follows:

Example Question #3 : Non Square Radicals

Rationalize the denominator and simplify: 

Possible Answers:

Correct answer:

Explanation:

To rationalize a denominator, multiply all terms by the conjugate. In this case, the denominator is , so its conjugate will be .

 

 

So we multiply: .

 

 

After simplifying, we get .

Example Question #4 : Non Square Radicals

Simplify: 

Possible Answers:

Correct answer:

Explanation:

Begin by getting a prime factor form of the contents of your root.

Applying some exponent rules makes this even faster:

Put this back into your problem:

Returning to your radical, this gives us:

Now, we can factor out  sets of  and  set of .  This gives us:

Example Question #5 : Non Square Radicals

Simplify:

Possible Answers:

Correct answer:

Explanation:

Begin by factoring the contents of the radical:

This gives you:

You can take out  group of .  That gives you:

Using fractional exponents, we can rewrite this:

Thus, we can reduce it to:

Or:

Example Question #6 : Non Square Radicals

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify , find the common factors of both radicals.

Sum the two radicals.

The answer is:  

Example Question #7 : Non Square Radicals

Simplify:

Possible Answers:

Correct answer:

Explanation:

To take the cube root of the term on the inside of the radical, it is best to start by factoring the inside:

Now, we can identify three terms on the inside that are cubes:

We simply take the cube root of these terms and bring them outside of the radical, leaving what cannot be cubed on the inside of the radical.

Rewritten, this becomes

Example Question #8 : Non Square Radicals

Simplify the radical:  

Possible Answers:

Correct answer:

Explanation:

Simplify both radicals by rewriting each of them using common factors.

Multiply the two radicals.

The answer is:  

Example Question #9 : Non Square Radicals

Simplify:  

Possible Answers:

Correct answer:

Explanation:

In order to simplify this radical, rewrite the radical using common factors.

Simplify the square roots.  

Multiply the terms inside the radical.

The answer is:  

Example Question #10 : Non Square Radicals

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Break down the two radicals by their factors.

A square root of a number that is multiplied by itself is equal to the number inside the radical.

Simplify the terms in the parentheses.

The answer is:  

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