Grade 8 Algebra: Word Problems: Square and Cube Roots

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Squares and cubes

1. Solve:
$\text{A}$ $\text{square}$ $\text{rug}$ $\text{has}$ $\text{an}$ $\text{area}$ $\text{of}$ $\text{36}$ $\text{square}$ $\text{feet.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{each}$ $\text{side?}$
2. Solve:
$\text{A}$ $\text{cube}$ $\text{box}$ $\text{has}$ $\text{a}$ $\text{volume}$ $\text{of}$ $\text{64}$ $\text{cubic}$ $\text{inches.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{each}$ $\text{edge?}$
3. Solve:
$\text{A}$ $\text{square}$ $\text{garden}$ $\text{has}$ $\text{an}$ $\text{area}$ $\text{of}$ $\text{81}$ $\text{square}$ $\text{meters.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{length}$ $\text{of}$ $\text{one}$ $\text{side?}$
4. Solve:
$\text{A}$ $\text{cube}$ $\text{of}$ $\text{ice}$ $\text{has}$ $\text{a}$ $\text{volume}$ $\text{of}$ $\text{27}$ $\text{cubic}$ $\text{cm.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{each}$ $\text{edge?}$
5. Solve:
$\text{A}$ $\text{square}$ $\text{tile}$ $\text{has}$ $\text{an}$ $\text{area}$ $\text{of}$ $\text{144}$ $\text{square}$ $\text{cm.}$ $\text{How}$ $\text{long}$ $\text{is}$ $\text{each}$ $\text{side?}$
6. Solve:
$\text{A}$ $\text{cube}$ $\text{tank}$ $\text{holds}$ $\text{1000}$ $\text{cubic}$ $\text{feet.}$ $\text{How}$ $\text{tall}$ $\text{is}$ $\text{it?}$
7. Solve:
$\text{A}$ $\text{square}$ $\text{photo}$ $\text{has}$ $\text{an}$ $\text{area}$ $\text{of}$ $\text{25}$ $\text{square}$ $\text{inches.}$ $\text{What}$ $\text{is}$ $\text{its}$ $\text{perimeter?}$
8. Solve:
$\text{A}$ $\text{cube}$ $\text{has}$ $\text{a}$ $\text{volume}$ $\text{of}$ $\text{125}$ $\text{cubic}$ $m\text{.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{area}$ $\text{of}$ $\text{one}$ $\text{face?}$

Answer Key

Level 1

1. $6\text{ ft}$
2. $4\text{ in}$
3. $9\text{ m}$
4. $3\text{ cm}$
5. $12\text{ cm}$
6. $10\text{ ft}$
7. $20\text{ in}$
8. $25\text{ m}^2$

Grade 8 Algebra: Word Problems: Square and Cube Roots

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Estimating and comparing

1. Solve:
$\text{A}$ $\text{square}$ $\text{room}$ $\text{has}$ $\text{an}$ $\text{area}$ $\text{of}$ $\text{50}$ $\text{square}$ $\text{ft.}$ $\text{Between}$ $\text{which}$ $\text{two}$ $\text{whole}$ $\text{numbers}$ $\text{is}$ $\text{its}$ $\text{side}$ $\text{length?}$
2. Solve:
$\text{A}$ $\text{cube}$ $\text{has}$ $\text{a}$ $\text{volume}$ $\text{of}$ $\text{30}$ $\text{cubic}$ $\text{cm.}$ $\text{Between}$ $\text{which}$ $\text{two}$ $\text{whole}$ $\text{numbers}$ $\text{is}$ $\text{its}$ $\text{edge?}$
3. Solve:
$\text{A}$ $\text{square}$ $\text{has}$ $\text{an}$ $\text{area}$ $\text{of}$ $\text{20}$ $\text{square}$ $m\text{.}$ $\text{Estimate}$ $\text{its}$ $\text{side}$ $\text{to}$ $\text{the}$ $\text{nearest}$ $\text{whole}$ $\text{meter.}$
4. Solve:
$\text{One}$ $\text{square}$ $\text{has}$ $\text{an}$ $\text{area}$ $\text{of}$ $\text{49}$ $\text{square}$ $\text{cm}$ $\text{and}$ $\text{a}$ $\text{bigger}$ $\text{square}$ $\text{has}$ $\text{an}$ $\text{area}$ $\text{of}$ $\text{64}$ $\text{square}$ $\text{cm.}$ $\text{How}$ $\text{much}$ $\text{longer}$ $\text{is}$ $\text{a}$ $\text{side}$ $\text{of}$ $\text{the}$ $\text{bigger}$ $\text{square?}$
5. Solve:
$\text{A}$ $\text{ladder}$ $\text{reaches}$ $\text{a}$ $\text{height}$ $\text{whose}$ $\text{square}$ $\text{is}$ $\text{90.}$ $\text{Is}$ $\text{the}$ $\text{height}$ $\text{more}$ $\text{or}$ $\text{less}$ $\text{than}$ $\text{9}$ $m\text{?}$
6. Solve:
$\text{A}$ $\text{cube}$ $\text{has}$ $\text{a}$ $\text{volume}$ $\text{of}$ $\text{8}$ $\text{cubic}$ $m\text{.}$ $\text{If}$ $\text{each}$ $\text{edge}$ $\text{is}$ $\text{doubled,}$ $\text{what}$ $\text{is}$ $\text{the}$ $\text{new}$ $\text{volume?}$
7. Solve:
$\text{A}$ $\text{square}$ $\text{has}$ $\text{an}$ $\text{area}$ $\text{of}$ $\text{2}$ $\text{square}$ $\text{units.}$ $\text{Is}$ $\text{its}$ $\text{side}$ $\text{rational}$ $\text{or}$ $\text{irrational?}$
8. Solve:
$\text{A}$ $\text{square}$ $\text{field}$ $\text{has}$ $\text{an}$ $\text{area}$ $\text{of}$ $\text{10000}$ $\text{square}$ $m\text{.}$ $\text{How}$ $\text{far}$ $\text{is}$ $\text{a}$ $\text{walk}$ $\text{around}$ $\text{it?}$

Answer Key

Level 3

1. $7\text{ and }8\text{ ft}$
2. $3\text{ and }4\text{ cm}$
3. $\approx 4\text{ m}$
4. $1\text{ cm}$
5. $\text{more } (\sqrt{90}>9)$
6. $64\text{ m}^3$
7. $\sqrt{2},\text{ irrational}$
8. $400\text{ m}$

Word Problems: Square and Cube Roots: Classroom Packet

Grade 8 Algebra: Word Problems: Square and Cube Roots

Level 1

Answer Key

Level 1

Grade 8 Algebra: Word Problems: Square and Cube Roots

Level 2

Answer Key

Level 2

Grade 8 Algebra: Word Problems: Square and Cube Roots

Level 3

Answer Key

Level 3