A Square and A Cube: Practice 1

Section A: Core Practice

Question 1mcq

Which arrangement represents the square number

81

?

A.A

1 \times 81

row

B.A

9 \times 10

rectangle

C.A stack of

81

cubes with unequal layers

D.A

9 \times 9

dot array

Question 2mcq

A teacher asks students to find

21^2

without a calculator. What is the value?

A.

441

B.

462

C.

42

D.

440

Question 3mcq

Riya only checks the unit digit of

238

. What can she conclude about whether it could be a perfect square?

A.Every number ending in that digit is definitely a square.

B.It must be a cube, not a square.

C.The unit digit test is never useful.

D.It cannot be a square based on the unit digit.

Question 4mcq

What is

\sqrt{225}

?

A.

16

B.

15

C.

14

D.

225

Question 5mcq

Between which two consecutive whole numbers does

\sqrt{120}

lie?

A.Between

11

and

12

B.Between

10

and

11

C.Exactly at

10

D.Between

9

and

10

Question 6mcq

A solid cube has

6

unit cubes along each edge. How many unit cubes are in the whole cube?

A.

36

unit cubes

B.

216

unit cubes

C.

36

unit cubes

D.

222

unit cubes

Section B: Reasoning and Application

Question 7mcq

What is

\sqrt[3]{64}

?

A.

16

B.

5

C.

4

D.

3

Question 8mcq

A school wants to arrange students in a square formation with

9

students in each row. How many students are needed?

A.

72

students

B.

729

students

C.

81

students

D.

36

students

Question 9mcq

Which arrangement represents the square number

81

?

A.A stack of

81

cubes with unequal layers

B.A

9 \times 9

dot array

C.A

1 \times 81

row

D.A

9 \times 10

rectangle

Question 10mcq

A teacher asks students to find

21^2

without a calculator. What is the value?

A.

440

B.

441

C.

462

D.

42

Question 11mcq

Riya only checks the unit digit of

238

. What can she conclude about whether it could be a perfect square?

A.It cannot be a square based on the unit digit.

B.The unit digit test is never useful.

C.It must be a cube, not a square.

D.Every number ending in that digit is definitely a square.

Question 12mcq

What is

\sqrt{225}

?

A.

16

B.

15

C.

14

D.

225