High School Math : Radicals

Study concepts, example questions & explanations for High School Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Expressing Radicals As Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and denominator to the exponent:

 

Simplify the expression by combining like terms:

 

 

Example Question #11 : Understanding Radicals

Express the following exponent in radical form:

Possible Answers:

Correct answer:

Explanation:

Begin by converting each exponent to have a denominator of :

 

Now, rearrange into radical form:

 

Finally, simplify:

Example Question #61 : Algebra Ii

Express the following exponent in radical form:

Possible Answers:

Correct answer:

Explanation:

Begin by converting each exponent to have a denominator of :

Now, put this in radical form:

Finally, simplify:

Example Question #62 : Algebra Ii

Simplify the following radical expression using exponents. Express the final answer in radical form.

Possible Answers:

Correct answer:

Explanation:

Begin by converting the radical into exponent form:

Simplify the exponent and multiply:

Convert into radical form:

Simplify:

 

Example Question #63 : Algebra Ii

Express the following exponent in radical form:

Possible Answers:

Correct answer:

Explanation:

Begin by changing the fractional exponents so that they both have a common denominator of :

Now, put this in radical form and simplify:

Example Question #1 : Simplifying 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 : Simplifying 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 : Simplifying 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 : 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:

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

Now, combine like terms:

Simplify:

Example Question #5 : Simplifying 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 

 

Learning Tools by Varsity Tutors