Algebra II : Multiplying and Dividing Radicals

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #61 : Multiplying And Dividing Radicals

Multiply:  

Possible Answers:

Correct answer:

Explanation:

It is possible to multiply all the integers together to form one radical, but doing so will give a square root of a value that will need to be factored.

Instead, rewrite each square root by their factors.  

A radical multiplied by itself will become the integer.  Simplify the expression.

The answer is:  

Example Question #61 : Multiplying And Dividing Radicals

Multiply the radicals:  

Possible Answers:

Correct answer:

Explanation:

Multiply the numbers in the radicals to combine as one radical.

This value can be simplified as a perfect square.

The answer is:  

Example Question #62 : Multiplying And Dividing Radicals

Multiply the radicals:  

Possible Answers:

Correct answer:

Explanation:

In order to multiply these radicals, we are allowed to multiply all three integers to one radical, but the final term will need to be simplified. 

Instead, we can pull out common factors in order to simplify the terms.

Rewrite the expression.

A radical multiplied by itself will give just the integer.

The answer is:  

Example Question #64 : Multiplying And Dividing Radicals

Divide the radicals:  

Possible Answers:

Correct answer:

Explanation:

Rationalize the denominator by multiplying the square root of 60 on the numerator and denominator.

Simplify the top and bottom of the fractions.

The radical can be simplified by using common factors of perfect squares.

Rewrite the term.

The answer is:  

Example Question #65 : Multiplying And Dividing Radicals

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

Since all terms are in radicals, we can simplify the terms by using common factors.

Rationalize the denominator.

The answer is:  

Example Question #161 : Simplifying Radicals

Multiply:  

Possible Answers:

Correct answer:

Explanation:

We can simplify the radicals before expanding by multiplication.

Simplify the radicals.

Multiply the integers together.  When a square root of a number is multiplied by itself, the radical will be eliminated, giving only the integer.

The answer is:  

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