What is the relationship between squares and square roots?

The square root of a number is the value that, when squared, returns the original number.

What is the relationship between cubes and cube roots?

The cube root of a number is the value that, when cubed, returns the original number.

How do you solve the equation $$x^2 = a$$ where $$a > 0$$ ?

Take the square root of $$a$$ to find @@x = ext{±} oot{a}@@.

How do you solve the equation $$x^3 = a$$ ?

Take the cube root of $$a$$ to find @@x = oot[3]{a}@@.

What is the formula for the area of a square?

The area of a square is given by the formula $$A = s^2$$ , where $$s$$ is the length of a side.

What is the formula for the volume of a cube?

The volume of a cube is given by the formula $$V = s^3$$ , where $$s$$ is the length of a side.

What does it mean for a number to be a perfect cube?

A perfect cube is a number that can be expressed as the cube of an integer.

What is the significance of negative solutions in equations like $$x^2 = a$$ or $$x^3 = a$$ ?

Negative solutions indicate that there are multiple values for $$x$$ that satisfy the equation, especially in the case of squares.

Resource Library

Math

Algebra

...

Solving Equations With Squares And Cubes

Solving Equations with Squares and Cubes

Flashcard

•

Mathematics

•

8th Grade

•

Practice Problem

•

Hard

•

CCSS

8.EE.A.2

Standards-aligned

Wayground Content

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16 questions

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FLASHCARD QUESTION

Front

What is the solution to the equation $x^2 = 36$ ?

Back

The solutions are $6$ and $-6$ .

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

What is the solution to the equation $x^3 = 64$ ?

Back

The solution is $4$ .

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

What is the value of $3^3$ ?

Back

The value is $27$ .

FLASHCARD QUESTION

Front

What is the solution to the equation $x^3 = -125$ ?

Back

The solution is $-5$ .

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

If the area of a square picture frame is 169 cm², what is the side length?

Back

The side length is $13 cm$ .

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

Define a perfect square.

Back

A perfect square is a number that can be expressed as the square of an integer.

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

What is the square root of a number?

Back

The square root of a number $x$ is a value that, when multiplied by itself, gives $x$ .

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

What is the cube of a number?

Back

The cube of a number $x$ is the result of multiplying $x$ by itself twice, or $x^3$ .

Tags

CCSS.8.EE.A.2

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