Algebra II : Multiplying and Dividing Radicals

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #11 : Multiplying And Dividing Radicals

Solve and simplify.

 

Possible Answers:

Correct answer:

Explanation:

When multiplying radicals, just take the values inside the radicand and perfom the operation.

 can't be reduced so this is the final answer.

Example Question #11 : Multiplying And Dividing Radicals

Solve and simplify.

Possible Answers:

Correct answer:

Explanation:

When multiplying radicals, just take the values inside the radicand and perfom the operation.

In this case, we have a perfect square so simplify that first.

Then, take that answer and multiply that with  to get the final answer.

.

 

Example Question #12 : Multiplying And Dividing Radicals

Solve and simplify.

Possible Answers:

Correct answer:

Explanation:

When dividing radicals, check the denominator to make sure it can be simplified or that there is a radical present that needs to be fixed. Since there is a radical present, we need to eliminate that radical. To do this, we multiply both top and bottom by . The reason is because we want a whole number in the denominator and multiplying by itself will achieve that. By multiplying itself, it creates a square number which can be reduced to .

With the denominator being , the numerator is . Final answer is .

 

 

 

Example Question #11 : Multiplying And Dividing Radicals

Solve and simplify.

Possible Answers:

Correct answer:

Explanation:

When dividing radicals, check the denominator to make sure it can be simplified or that there is a radical present that needs to be fixed.

Both  and  are perfect squares so they can be simplify.

Final answer is

 .

Example Question #15 : Multiplying And Dividing Radicals

Solve and simplify.

Possible Answers:

Correct answer:

Explanation:

When multiplying radicals, just take the values inside the radicand and perfom the operation.

Since there is a number outside of the radicand, multiply the outside numbers and then the radicand.

Example Question #12 : Multiplying And Dividing Radicals

Solve and simplify.

Possible Answers:

Correct answer:

Explanation:

When multiplying radicals, just take the values inside the radicand and perfom the operation.

Since there is a number outside of the radicand, multiply the outside numbers and then the radicand. 

Before we say that's the final answer, check the radicand to see that there are no square numbers that can be factored. A  can be factored and thats a perfect square. When I divide  with , I get  which doesn't have perfect square factors.

Therefore, our answer becomes

 

Example Question #17 : Multiplying And Dividing Radicals

Solve and simplify.

Possible Answers:

Correct answer:

Explanation:

When multiplying radicals, just take the values inside the radicand and perfom the operation.

Since there is a number outside of the radicand, multiply the outside numbers and then the radicand. 

 

Example Question #18 : Multiplying And Dividing Radicals

Solve and simplify.

Possible Answers:

Correct answer:

Explanation:

Since we are dealing with exponents, lets break it down.

Remember to distribute.

Example Question #11 : Multiplying And Dividing Radicals

Solve and simplify.

Possible Answers:

Correct answer:

Explanation:

When dividing radicals, check the denominator to make sure it can be simplified or that there is a radical present that needs to be fixed. Since there is a radical present, we need to eliminate that radical. However, there is a faster way to possibly elminate the denominator. Let's simplify the numerator.

.

The reason I split it up is because I can cancel out the radicals and thus simplifying the question to give final answer of .

Example Question #13 : Multiplying And Dividing Radicals

Solve and simplify.

Possible Answers:

Correct answer:

Explanation:

When dividing radicals, check the denominator to make sure it can be simplified or that there is a radical present that needs to be fixed. Since there is a radical present, we need to eliminate that radical. However, there is a faster way to possibly elminate the denominator. Let's simplify the numerator.

We still need to eliminate the radical so multiply top and bottom by .

.

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