Algebra II : Square Roots

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #11 : Radicals

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Rewrite the radical using common factors.

Recall that  is equivalent to the imaginary term .

Simplify the roots.

The answer is:  

Example Question #12 : Radicals

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

Evaluate each square root.  The square root of the number is equal to a number multiplied by itself.

The answer is:  

Example Question #11 : Square Roots

Simplify the radicals:  

Possible Answers:

Correct answer:

Explanation:

Simplify each radical.  A number inside the radical means that we are looking for a number times itself that will equal to that value inside the radical.

For a fourth root term, we are looking for a number that multiplies itself four times to get the number inside the radical.

Replace the values and determine the sum.

The answer is:  

Example Question #13 : Radicals

Simplify the radicals:  

Possible Answers:

Correct answer:

Explanation:

Do not multiply the terms inside the radical.  Instead, the terms inside the radical can be simplified term by term.

Simplify each square root.

The answer is:  

Example Question #14 : Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Solve by evaluating the square roots first.  

Substitute the terms back into the expression.

The answer is:  

Example Question #15 : Radicals

Solve the square roots: 

Possible Answers:

Correct answer:

Explanation:

Evaluate each radical.  The square root of a certain number will output a number that will equal the term inside the radical when it's squared.

Replace all the terms.

The answer is:  

Example Question #16 : Radicals

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

This expression is imaginary.  To simplify, we will need to factor out the imaginary term  as well as the perfect square.

Simplify the terms.

The answer is:  

Example Question #18 : Radicals

Solve:  

Possible Answers:

Correct answer:

Explanation:

Evaluate each square root.  The square root identifies a number that multiplies by itself to equal the number inside the square root.

Determine the sum.

The answer is:  

Example Question #17 : Radicals

Evaluate, if possible:  

Possible Answers:

Correct answer:

Explanation:

The negative numbers inside the radical indicates that we will have imaginary terms.

Recall that .

Rewrite the radicals using  as the common factor.

Replace the terms and evaluate the square roots.

The answer is:  

Example Question #18 : Radicals

Simplify:  

Possible Answers:

Correct answer:

Explanation:

Evaluate by solving each square root first.  The square root of a number is a number that multiplies by itself to achieve the number inside the square root.

Rewrite the expression.

The answer is:  

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