High School Math : Radicals

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #6 : Simplifying 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 : Simplifying 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 : Simplifying 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 : Simplifying 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 : Simplifying 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:

Example Question #11 : Factoring Radicals

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by factoring the radicals and combining like terms:

Multiply the left side of the equation by  and the right side by :

Example Question #12 : Factoring Radicals

Simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by factoring the integer:

Factor the exponents:

Example Question #13 : Factoring Radicals

Simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by factoring the integer:

Factor the exponents:

Example Question #14 : Factoring Radicals

Simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by factoring the integer:

Factor the exponents:

Example Question #15 : Factoring Radicals

Simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by factoring the expression:

Now, take the square root:

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