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Common Core: 8th Grade Math : cube roots

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

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All Common Core: 8th Grade Math Resources

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Example Questions

Example Question #1 : Cube Roots

$\small 76a^3+19a^2+16a=-4$

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

Possible Answers:

$\small \left\{-\frac{1}{2}\right\}$

$\small \small \left\{-2, 2\right\}$

$\small \left\{-\frac{4}{19}, \frac{4}{19}\right\}$

$\small \left\{-\frac{1}{4}\right\}$

$\small \left\{\frac{19}{4} \right \}$

Correct answer:

$\small \left\{-\frac{1}{4}\right\}$

Explanation:

Rewriting the equation as $\small 76a^3+19a^2+16a+4=0$ , 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 $\small 19a^2$ and between the third and fourth terms, the GCF is 4. Thus, we obtain $\small \small 19a^2(4a+1)+4(4a+1)=0 \rightarrow (4a+1)(19a^2+4)=0$ . Setting each factor equal to zero, and solving for $\small a$ , we obtain $\small a=-\frac{1}{4}$ from the first factor and $\small a^2=-\frac{4}{19}$ from the second factor. Since the square of any real number cannot be negative, we will disregard the second solution and only accept $\small a=-\frac{1}{4}$ .

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Example Question #2 : Cube Roots

Solve for $x\textup:$

x^3=8

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:

$\sqrt[3]{x}=\sqrt[3]{8}$

x=2

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Example Question #3 : Cube Roots

Solve for $x\textup:$

x^3=64

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 64? "

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:

$\sqrt[3]{x}=\sqrt[3]{64}$

x=4

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Example Question #4 : Cube Roots

Solve for $x\textup:$

x^3=27

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 27? "

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:

$\sqrt[3]{x}=\sqrt[3]{27}$

x=3

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Example Question #5 : Cube Roots

Solve for $x\textup:$

x^3=216

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 216? "

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:

$\sqrt[3]{x}=\sqrt[3]{216}$

x=6

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Example Question #6 : Cube Roots

Solve for $x\textup:$

x^3=125

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 125? "

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:

$\sqrt[3]{x}=\sqrt[3]{125}$

x=5

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Example Question #7 : Cube Roots

Solve for $x\textup:$

x^3=343

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 343? "

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:

$\sqrt[3]{x}=\sqrt[3]{343}$

x=7

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Common Core: 8th Grade Math : cube roots

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

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #1 : Cube Roots

Example Question #2 : Cube Roots

Example Question #3 : Cube Roots

Example Question #4 : Cube Roots

Example Question #5 : Cube Roots

Example Question #6 : Cube Roots

Example Question #7 : Cube Roots

All Common Core: 8th Grade Math Resources

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