High School Math : Factoring Radicals

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #1 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by factoring the integer:

Now, simplify the exponents:

Example Question #2 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by converting the radical into exponent form:

Now, multiply the exponents:

Example Question #3 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by converting the radical into exponent form:

Now, combine the bases:

Simplify the integer:

Now, simplify the exponents:

 

Convert back into radical form and simplify:

Example Question #4 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by multiplying the numerator and denominator by the complement of the denominator:

Use the FOIL method to multiply the radicals. F (first) O (outer) I (inner) L (last)

Now, combine like terms:

Simplify:

Example Question #5 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by factoring the radicals:

Combine like terms:

Multiply the left side by  and the right side by 

 

Example Question #6 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by converting the radicals into exponent form:

Now, combine the bases:

Convert back into radical form and simplify:

Example Question #7 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by simplifying the right side of the rational expression:

 

Now, combine like terms:

Example Question #8 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by using the FOIL method to multiply the radical expression. F (first) O (outer) I (inner) L (last)

Now, combine like terms:

Example Question #9 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by multiplying the numerator and denominator by :

The expression cannot be further simplified.

Example Question #10 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by multiplying the numerator and denominator by the complement of the denominator:

Combine like terms and simplify:

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