High School Math : Simplifying Radicals

Study concepts, example questions & explanations for High School Math

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Example Questions

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:

Example Question #16 : Factoring Radicals

Simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Simplify the radical expression:

Example Question #1 : Simplifying Radicals

Simplify the expression:

Possible Answers:

.

Correct answer:

Explanation:

Use the multiplication property of radicals to split the fourth roots as follows:

Simplify the new roots:

Example Question #2 : Adding And Subtracting Radicals

Find the value of .

Possible Answers:

Correct answer:

Explanation:

To solve this equation, we have to factor our radicals.  We do this by finding numbers that multiply to give us the number within the radical. 

Add them together:

4 is a perfect square, so we can find the root:

Since both have the same radical, we can combine them:

Example Question #81 : Algebra Ii

Factor and simplify the following radical expression:

Possible Answers:

Correct answer:

Explanation:

Begin by using the FOIL method (First Outer Inner Last) to expand the expression.

Now, combine like terms:

Example Question #1 : Using Radicals With Elementary Operations

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

When combining terms involving radicals, we can only combine the ones that have the same radical.  For this problem, that means  has to stay on its own while we can combine  and  into .  The simple integers can be combined too, giving us our answer with three seperate terms.

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