Task Sets: Use square root and cube root symbols to represent solutions to equations - Common Core Math - Grade 8

A

Recall / Warm-Up

1.

What is the value of $7^2$ ?

A.

14

B.

49

C.

3.5

D.

72

2.

What is the value of $4^3$ ?

A.

12

B.

16

C.

64

D.

81

B

Fluency Practice

1.

Which of the following are all the real solutions to the equation $x^2 = 49$ ?

A.

$x = 7$

B.

$x = -7$

C.

$x = 49$

D.

$x = \pm 7$

2.

Evaluate $\sqrt{121}$ .

3.

Solve the equation $x^3 = 64$ .

4.

Evaluate $\sqrt[3]{125}$ .

5.

Evaluate $\sqrt{\frac{9}{16}}$ .

6.

Solve the equation $x^2 = \frac{25}{36}$ .

A.

$x = \frac{5}{6}$

B.

$x = \pm \frac{5}{6}$

C.

$x = \frac{25}{6}$

D.

$x = \pm \frac{6}{5}$

C

Varied Practice

D

Word Problems

$Square garden with area 144$

1.

A square-shaped community garden has an area of 144 square meters.

What is the side length of the garden, in meters?

$Cube crate with volume 8$

2.

A shipping crate is in the shape of a cube and has a volume of 8 cubic feet.

What is the length of one edge of the crate, in feet?

$Square with area 2 and a diagonal$

3.

Consider a square with an area of 2 square units.

1.

What is the exact side length of the square? (Use the square root symbol in your answer if needed.)

2.

Is the side length of this square a rational or irrational number?

A.

Rational

B.

Irrational

E

Error Analysis

1.

A student was asked to evaluate $\sqrt{25}$ . They wrote:
$\sqrt{25} = \pm 5$

Is the student's statement correct? Why or why not?

A.

Yes, because $5^2 = 25$ and $(-5)^2 = 25$ .

B.

No, the symbol $\sqrt{}$ always refers to the principal (non-negative) root.

C.

No, $\sqrt{25}$ is only equal to -5.

D.

Yes, square roots always have two answers.

2.

To solve the equation $x^3 = 27$ , a student wrote:
$x = \pm 3$

Identify the error in the student's work.

A.

The student should have written $x = 9$ .

B.

Cube roots do not have a negative solution when the constant is positive, because $(-3)^3 = -27$ , not $27$ .

C.

The student should have used the square root symbol.

D.

There is no error; $x = \pm 3$ is correct.

F

Challenge / Extension

1.

A student says that $\sqrt{2}$ is rational because a calculator shows it is 1.41421356, which is a terminating decimal. Explain why this reasoning is incorrect.

2.