Power Play: Squares, Cubes, and Number Patterns

Question 1

Which number is both a perfect square and a perfect cube, while lying strictly between 50 and 100?

Accepted Answer

64

Answer

72

Answer

81

Answer

96

Question 2

If n is doubled, by what factor does n^3 change?

Accepted Answer

It becomes 8 times as large

Answer

It doubles

Answer

It becomes 4 times as large

Answer

It becomes 16 times as large

Question 3

Which expression is equal to 3^2 × 3^3?

Accepted Answer

3^5

Answer

3^6

Answer

9^5

Answer

6^5

Question 4

The difference between consecutive squares follows which pattern: 1^2 to 2^2, 2^2 to 3^2, 3^2 to 4^2, and so on?

Accepted Answer

Consecutive odd numbers

Answer

Consecutive even numbers

Answer

Prime numbers only

Answer

Multiples of 3

Question 5

Which number can be written as both 2^6 and 4^3?

Accepted Answer

64

Answer

32

Answer

48

Answer

81

Question 6

A cube has its edge length tripled. How does its volume change?

Accepted Answer

It becomes 27 times the original

Answer

It becomes 6 times the original

Answer

It becomes 9 times the original

Answer

It becomes 18 times the original

Question 7

Which of the following is the sum of two consecutive perfect squares?

Accepted Answer

41

Answer

45

Answer

49

Answer

53

Question 8

If x^2 = 49 and x is negative, what is x^3?

Accepted Answer

-343

Answer

-147

Answer

147

Answer

343

Question 9

Which statement about perfect squares and perfect cubes is true for positive integers?

Accepted Answer

Some numbers are both, such as powers of six in the exponent

Answer

Every perfect cube is also a perfect square

Answer

Every perfect square is also a perfect cube

Answer

No positive integer can be both a perfect square and a perfect cube

Question 10

What is the value of 5^2 + 2^3?

Accepted Answer

33

Answer

29

Answer

31

Answer

35

Power Play: Squares, Cubes, and Number Patterns

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