# Common Core: 8th Grade Math : Use and Evaluate Square Roots and Cube Roots: CCSS.Math.Content.8.EE.A.2

## Example Questions

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13

10

56

0

14

14

Explanation:

If , then .

Therefore, .

### Example Question #1 : Equations / Solution Sets

Solve the equation:

Explanation:

Rewriting the equation as , we can see there are four terms we are working with, so factor by grouping is an apporpriate method. Between the first two terms, the 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 #1 : How To Factor An Equation

Solve the equation:

Explanation:

Add 8 to both sides to set the equation equal to 0:

To factor, find two integers that multiply to 24 and add to 10.  4 and 6 satisfy both conditions. Thus, we can rewrite the quadratic of three terms as a quadratic of four terms, using the the two integers we just found to split the middle coefficient:

Then factor by grouping:

Set each factor equal to 0 and solve:

and

### Example Question #11 : How To Factor An Equation

Solve by completing the square:

no real solution

Explanation:

In order to set this up for completing the square, we need to move the 135 to the other side:

Now the equation is in the form:

To complete the square we need to add to both sides the folowing value:

So we need to add 9 to both sides of the equation:

Now we can factor the left side and simplify the left side:

Now we need to take the square root of both sides:

**NOTE: Don't foget to add the plus or minus symbol. We add this becase there are two values we can square to get 144:

and

**End note

Now we can split into two equations and solve for x:

and

So our solution is:

### Example Question #1 : Use And Evaluate Square Roots And Cube Roots: Ccss.Math.Content.8.Ee.A.2

Solve for

Explanation:

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

"What number squared 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  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 squaring a number, which is taking the square root:

### Example Question #3 : Use And Evaluate Square Roots And Cube Roots: Ccss.Math.Content.8.Ee.A.2

Solve for

Explanation:

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

"What number squared 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 squaring a number, which is taking the square root:

### Example Question #1 : Use And Evaluate Square Roots And Cube Roots: Ccss.Math.Content.8.Ee.A.2

Solve for

Explanation:

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

"What number squared 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 squaring a number, which is taking the square root:

### Example Question #1 : Use And Evaluate Square Roots And Cube Roots: Ccss.Math.Content.8.Ee.A.2

Solve for

Explanation:

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

"What number squared 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 squaring a number, which is taking the square root:

### Example Question #9 : Use And Evaluate Square Roots And Cube Roots: Ccss.Math.Content.8.Ee.A.2

Solve for

Explanation:

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

"What number squared 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 squaring a number, which is taking the square root:

### Example Question #1 : Use And Evaluate Square Roots And Cube Roots: Ccss.Math.Content.8.Ee.A.2

Solve for

Explanation:

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

"What number squared 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 squaring a number, which is taking the square root:

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