cube roots - 8th Grade Math

Card 0 of 28

Question

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

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

Answer

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 $\small a=-\frac{1}{4}$ .

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

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

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

Answer

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 $\small a=-\frac{1}{4}$ .

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

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

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

Answer

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 $\small a=-\frac{1}{4}$ .

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

Question

Solve for $x\textup:$

Answer

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:

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

Compare your answer with the correct one above

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