Common Core: 8th Grade Math : Grade 8

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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Example Questions

Example Question #7 : Square Roots

Which of the following is equal to ?

Possible Answers:

Correct answer:

Explanation:

When you're asked to take the square root of a number, the question is asking "which number, when squared, gives you this number?"  Here they're asking, then, which number times itself will produce .  The answer, then, is  , since .

With roots, you can also use the rule that the square root of an entire fraction is equal to the square root of the numerator divided by the square root of the denominator.  Here that means that  is equal to .  And the square roots of 1 and 4 are each integers, so that allows you to calculate to the answer .

Example Question #1 : Cube Roots

Which of the following displays the full real-number solution set for  in the equation above?

Possible Answers:

Correct answer:

Explanation:

Rewriting the equation as , we can see there are four terms we are working with, so factor by grouping is an appropriate method. Between the first two terms, the Greatest Common Factor (GCF) is  and between the third and fourth terms, the GCF is 4. Thus, we obtain .   Setting each factor equal to zero, and solving for , we obtain  from the first factor and  from the second factor. Since the square of any real number cannot be negative, we will disregard the second solution and only accept 

Example Question #581 : Grade 8

Solve for 

 

Possible Answers:

Correct answer:

Explanation:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically. 

In order to solve this problem using algebra, we need to isolate the  on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cubed root:

Example Question #582 : Grade 8

Solve for 

 

Possible Answers:

Correct answer:

Explanation:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically. 

In order to solve this problem using algebra, we need to isolate the  on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cubed root:

Example Question #583 : Grade 8

Solve for 

 

Possible Answers:

Correct answer:

Explanation:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically. 

In order to solve this problem using algebra, we need to isolate the  on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cubed root:

Example Question #5 : Cube Roots

Solve for 

 

Possible Answers:

Correct answer:

Explanation:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically. 

In order to solve this problem using algebra, we need to isolate the  on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cubed root:

Example Question #584 : Grade 8

Solve for 

 

Possible Answers:

Correct answer:

Explanation:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically. 

In order to solve this problem using algebra, we need to isolate the  on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cube root:

Example Question #585 : Grade 8

Solve for 

Possible Answers:

Correct answer:

Explanation:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically. 

In order to solve this problem using algebra, we need to isolate the  on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cube root:

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