Algebra II : Understanding Radicals

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #31 : Understanding Radicals

Simplify:  

Possible Answers:

Correct answer:

Explanation:

In order to simplify this radical, rewrite the radical using common factors.

Simplify the square roots.  

Multiply the terms inside the radical.

The answer is:  

Example Question #32 : Understanding Radicals

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Break down the two radicals by their factors.

A square root of a number that is multiplied by itself is equal to the number inside the radical.

Simplify the terms in the parentheses.

The answer is:  

Example Question #33 : Understanding Radicals

Simplify, if possible:  

Possible Answers:

Correct answer:

Explanation:

The first term is already simplified.  The second and third term will need to be simplified.

Write the common factors of the second radical and simplify.

Repeat the process for the third term.

Rewrite the expression.

Combine like-terms.

The answer is:  

Example Question #34 : Understanding Radicals

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Simplify the first term by using common factors of a perfect square.

Simplify the second term also by common factors.

Combine the terms.

The coefficients cannot be combined since these are unlike terms.

The answer is:  

Example Question #35 : Understanding Radicals

Simplify:  

Possible Answers:

Correct answer:

Explanation:

To simplify this, multiply the top and bottom by the denominator.

Reduce the fraction.

The answer is:  

Example Question #36 : Understanding Radicals

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's .

.

Example Question #37 : Understanding Radicals

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's .

Example Question #38 : Understanding Radicals

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's .

Example Question #39 : Understanding Radicals

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's .

Example Question #40 : Understanding Radicals

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Multiply the radicals.

Simplify this by writing the factors using perfect squares.

Multiply this with the integers.

The answer is:  

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