Squares, Cubes, & Radicals

Square Root

100

What is the positive square root of 25?

5

200

What is the positive AND negative square root of 121?

11 and -11

300

Find the square root of 78?

Round to the nearest hundredth. 

8.83

400

85 is a root of what perfect square?

7225

500

What is the square root of 196^-1  

1/14 or 14^-1

Cube Root

100

What is the cube root of 27?

3

200

What is the cube root of 8?

2

300

Find the cube root of 890?

Round to the nearest hundredth.

9.62

400

25 is a root of what perfect cube?

15,625

500

What is the cube root of 4096^-1

1/16 or 16^-1

Roots on a Number Line

100

What two numbers does the square root of 14 fall between?

A. 1 and 2 

B. 2 and 3

C. 3  and 4

D. 5 and 6

C. 3 and 4 because it is approximately 3.7

200

What two numbers will the cube root of 89 fall between?

A. 4 and 5

B. 5 and 6

C. 6 and 7

D. 7 and 8

A. 4 and 5 because it is approximately 4.5. 

300

Which of the points on the number line could represent the square root of 20?

(look at number line)

Point K because the square root of 20 is approximately 4.5. 

400

Which of the points on the number line could represent the square root of 16?

(look at the number line)

Point G because the square root of 16 is 4 AND -4. 

500

Could the square root of 35 fall between 6 and 8?

NO because the square root of 35 is approximately 5.9. So it would fall between 5 and 6. 

Equations With Radicals

100

solve for x.

x²=49

x=7

200

Solve for x.

x³=1728

x=12

300

Solve for x.

x³+12=524

x=8

400

solve for x

-3x³+14=-67    

x=3

500

Solve for x.

x(x+4)-3=4(x+19.5)

x=9

Word Problems

100

The area of a square shaped yard is 25 ft².

What is the length of one of the sides?

Side length would be 5ft. 

200

Jacob is buying a rubix cube. If the volume of the cube is 27 cm³, what would be the height of the cube? (a side length)

The height of the cube would be 3 cm. 

300

If the side length of a square is 3x, and the area of the square is 36, solve for x. 

x=2

400

A square decorative tile has an area of 121 cm². What is the length and width of the tile?

length=11 cm

width=11cm

500

Katie is buying cube shaped blocks to add to her shelf of decorations. She needs the dimensions of the cube to be less than 4 inches along each edge. Which of the following would work according to the size she needs?

A. cubes with a volume of 27 in³

B. Cubes with a volume of 64 in³

C. Cubes with a volume of 125 in³

D. Both A and B would work

A. because 4³ = 64 in³

The volume of the cube need to be LESS than 64.