Solve the equation $$\text{cbrt}(x) = 6$$ . What is x?

x = 216, because $$6^3 = 216$$ .

If $$\text{sqrt}(x) - 8 = -3$$ , what is x?

x = 25, because $$\text{sqrt}(25) - 8 = -3$$ .

How do you isolate the variable in the equation $$\text{sqrt}(x + 2) = 3$$ ?

Square both sides to get $$x + 2 = 9$$ , then solve for x.

What happens when you square both sides of an equation?

Squaring both sides can introduce extraneous solutions, so always check your solutions.

What is an extraneous solution?

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Solve $$\text{cbrt}(x) = -4$$ . What is x?

x = -64, because $$(-4)^3 = -64$$ .

What is the domain of the square root function?

The domain of the square root function is all non-negative real numbers, i.e., $$x \geq 0$$ .

What is the relationship between square roots and squaring a number?

Squaring a number and taking the square root are inverse operations. If $$y = \text{sqrt}(x)$$ , then $$y^2 = x$$ .

Unit 3 Lesson 9: Solving Cube and Square Roots Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the square root of a number?

Back

Tags

CCSS.8.EE.A.2

2.

FLASHCARD QUESTION

Front

Can the square root of a negative number be a real number?

Back

No, the square root of a negative number is not a real number. It is an imaginary number.

Tags

CCSS.HSN.CN.A.1

3.

FLASHCARD QUESTION

Front

What is the cube root of a number?

Back

Tags

CCSS.8.EE.A.2

4.

FLASHCARD QUESTION

Front

Back

There is NO SOLUTION because the square root of a number cannot be negative.

Tags

CCSS.HSA.REI.A.2

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.A.2

7.

FLASHCARD QUESTION

Front

What is the principal square root?

Back

Tags

CCSS.8.EE.A.2

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