Worksheet

Weekend Bike Repair: Root Checks

Practice square and cube roots, solve power equations, and identify irrational roots through a student-run bike-repair business.

Grade 8MathInteractive · Printable

Aligned to8.EE.A.2

Play online Play as a game

PrintLetter-size worksheet Answer keyPrintable answers

Assign to classAssign to your classes, or get a join code

What’s included

Single worksheet
Auto-graded online
1 Common Core standard
Printable answer key
14 questions
Classroom-ready

Details

Format: Interactive · Printable
Grade: Grade 8
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

Students evaluate square and cube roots of small perfect squares and cubes.
Students solve equations of the forms x² = p and x³ = p using root symbols.
Students identify √2 as irrational and distinguish equation solutions from principal square roots.

How to use

Use for independent practice after introducing root symbols. Have students work without calculators, then discuss the final error analysis.

Curriculum

Common Core standard covered

8.EE.A.2

Use square and cube root symbols to solve x^2 = p and x^3 = p, find roots of small perfect squares and cubes, and know root 2 is irrational.

Preview

OwlSheets.com

Name Date

Weekend Bike Repair: Root Checks

Use square and cube roots to check workshop plans.

Bench Checks

Maya and Luis run a weekend bike-repair business. Complete their math checks without a calculator. The symbol √ means the nonnegative square root.

Evaluate each root.

√169 = ∛216 =

Which statement correctly evaluates −√100?

A. It has no real value.
B. Its values are −10 and 10.
C. Its value is −10.
D. Its value is 10.

∛(−1000) =

Which choice lists all real solutions of x² = 49/64?

A. x = −7/32 or x = 7/32
B. x = −49/64 or x = 49/64
C. x = 7/8 only
D. x = −7/8 or x = 7/8

Solve x³ = 1/8. Write your answer as a fraction.

x =

Equation Checks

Pay attention to whether an equation contains a square or a cube. Include every real solution when asked.

Solve x² = 225.

Negative solution: x =
Positive solution: x =

Which choice lists all real solutions of x³ = −729?

A. x = −9 only
B. x = −9 or x = 9
C. x = −243 only
D. x = 9 only

Maya compares √64 and ∛64. Which statement is correct?

A. √64 is 8, and ∛64 is 4.
B. √64 is 8, and ∛64 is 8.
C. √64 is 4, and ∛64 is 8.
D. √64 is 32, and ∛64 is 16.

Select every equation that has exactly two real solutions.

x² = 16x³ = 27x² = 0x² = 1/4x³ = −1

Workshop Decisions

Apply roots to the repair business. Use positive values for physical lengths.

10.

Luis cuts a square protective mat with an area of 196 square inches. If its side length is x inches, then x² = 196.

How long is each side? inches

11.

Maya buys a solid rubber cube to use as a protective support. Its volume is 125 cubic centimeters. If its edge length is x centimeters, then x³ = 125.

What is the cube's edge length? cm

12.

The students want a square business sign with an area of 2 square feet. Its side length x must satisfy x² = 2. Which description gives the exact side length?

A. The side is 1 foot, a rational length.
B. The side is √2 feet, an irrational length.
C. The side is 2 feet, a rational length.
D. The side is √2 feet, a rational length.

13.

Select every expression whose value is irrational.

√2√(4/9)−√2∛(−8)√0

14.

On a practice sheet, Luis writes, “x³ = −125 has two solutions, −5 and 5, because taking a root always gives a positive and a negative answer.” Explain his mistake. Give the correct solution using a cube root symbol and check both proposed values.