All Common Core: 8th Grade Math Resources
Example Questions
Example Question #7 : Square Roots
Which of the following is equal to ?
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?
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
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
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
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
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
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
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: