Numerical Roots and Radicals Chapter Questions



Equations with Roots and Radicals Chapter Questions

1. Why would we simplify a non-perfect square root instead of just estimating it?

2. How do you solve an equation with perfect square and cube roots?

Equations with Roots and Radicals Chapter Problems

Squares, Square Roots & Perfect Squares

Classwork

Radical Expressions Containing Variables

1. Simplify

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

Homework

2. Simplify

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

Simplifying Non-Perfect Square Radicands

Classwork

3. Simplify

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

i. [pic]

j. [pic]

k. [pic]

l. [pic]

m. [pic]

4. When [pic] is written in simplest radical form, the result is [pic]. What is the value of k?*

5. When [pic] is expressed in simplest [pic] form, what is the value of a? What is the value of b?*

6. Circle the number that is greater*

a. [pic] or 5

b. [pic] or -6

c. [pic] or 10

d. [pic] or -15

Homework

7. Simplify

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

i. [pic]

j. [pic]

k. [pic]

l. [pic]

m. [pic]

8. When [pic] is written in simplest radical form, the result is [pic]. What is the value of k?*

9. When [pic] is expressed in simplest [pic] form, what is the value of a? What is the value of b?*

10. Circle the number that is greater

a. [pic] or 7

b. [pic] or -6

c. [pic] or 12

d. [pic] or -9

Simplifying Roots of Variables

Classwork

11. Simplify

a.[pic]

b.[pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

i. [pic]

j. [pic]

k. [pic]

Homework

12. Simplify

a.[pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

i. [pic]

Solving Equations with Perfect Squares and Cube Roots

Classwork

13. Solve.

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. 25+x2=50

g. x3- 10=54

14. A cube has a volume of 512cm3. A) Write an equation that could be used to determine the length, L, of one side of the cube. B) Solve the equation.*

15. Estimate the area of a rectangle with a length of [pic] inches and a width of 10 inches to the nearest tenth.*

16. If the area of a square is [pic] in2. What is the length of one side of the square?*

17. Which equation has -8 as a possible value of x?

a. x3 = -512

b. x2 = -64

c. x3 = -16

d. x2 = -16

Homework

18. Solve.

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]x2 = 90

g. x3+ 5 = -120

19. A cube has a volume of 216cm3. A) Write an equation that could be used to determine the length, L, of one side of the cube. B) Solve the equation.*

20. Estimate the area of a rectangle with a length of [pic] inches and a width of 4 inches to the nearest tenth.*

21. If the area of a square is [pic] in2. What is the length of one side of the square?*

22. Which equation has both 6 and -6 as possible values of x?

a. x2 = 12

b. x3 = 18

c. x2 = 36

d. x3 = 216

Equations with Roots & Radicals Review

1) [pic] [pic] *

a. >

b. <

c. =

2) Simplify: [pic]

a. 40[pic]

b. 2[pic]

c. 3[pic]

d. 9[pic]

3) When [pic] is written in simplest radical form, the result is [pic]. What is the value of k?*

a. 20 c. 14

b. 40 d. 4

4) When [pic] is written in simplest radical form, [pic]. What is the value of a? What is the value of b?*

5) Solve: [pic]

6) Solve: [pic]

7) [pic] ___________________

8) [pic] _____________________

9) Simplify [pic]____________

10) Approximate the area of a rectangle to the nearest tenth if its length is [pic]cm and its width is [pic] cm.*

11) A cube has a side length of 2x and a volume of 216 cm3.*

a. Write an equation for the volume of the cube.

b. Solve the equation to find the value of x.

Answer Key

1.

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

2.

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

3.

a. 5[pic]

b. 4[pic]

c. 2[pic]

d. 2[pic]

e. 5[pic]

f. 10[pic]

g. 5[pic]

h. 2[pic]

i. 3[pic]

j. 6[pic]

k. 105[pic]

l. 33[pic]

m. 66[pic]

4. K=28

5. A=2, b=14

6.

a. 5

b. -6

c. [pic]

d. [pic]

7.

a. 4[pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

i. [pic]

j. [pic]

k. [pic]

l. [pic]

m. [pic]

8. K=30

9. a=5, b=5

10.

a. 7

b. -6

c. [pic]

d. [pic]

11.

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

[pic]

f. [pic]

g. [pic]

h. [pic]

i. [pic]

j. [pic]

12.

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

i. [pic]

13.

a. 2

b. ±14

c. -5

d. ±12

e. ±7

f. ±5

g. 4

14. a. L3=512 b. L=8cm

15. ~120in2

16. [pic]in

17. a

18.

a. -1

b. ±25

c. ±6

d. -3

e. 4

f. ±9

g. -5

19. a. L3= 216 b. L=6cm

20. ~44.8in2

21. [pic]in

22. c

Review answers

1. a

2. c

3. b

4. a=3, b=14

5. ±6

6. -6

7. 5x7y[pic]

8. 10xyz2[pic]

9. x5

10. ~44cm2

11. a. [pic] =216

b. x=3cm

* From Engage NY

* From Engage NY

* From Engage NY

* From Engage NY

* From Engage NY

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