4.i Perfect Squares + Cubes

Question 1

The square root of a perfect square will always be _____________

Answer 1

The square root of a perfect square will always be an integer.

Question 2

What are the first nine perfect squares?

Answer 2

0, 1, 4, 9, 16, 25, 36, 49, 64

Question 3

All perfect squares must end in ________ (units digit)

Answer 3

All perfect squares must end in 0, 1, 4, 5, 6, or 9,

Question 4

A perfect square (other than 0 and 1), is a number such that all its prime factors have _______ exponents

Answer 4

Even exponents

Question 5

Which perfect squares must always have its prime factors have even exponents?

Answer 5

All perfect squares (aside from 0 and 1)

Question 6

How would you answer this?

Answer 6

To make a perfect square, z must contribute to the missing factors.

Remember, a perfect square requires even exponents in its prime factors.

So, 3 x 5 x 7 = 105 (this is the final answer).

Question 7

What is a perfect cube?

Answer 7

A number who’s cube root is an integer

Question 8

Is 8 a perfect cube?

Answer 8

Yes! 8 is a perfect cube, considering the cube root of 8, is 2, which is an integer

Question 9

If some number x is a perfect cube, the prime factorization must contain only exponents that are multiples of ___

Answer 9

If some number x is a perfect cube, the prime factorization must contain only exponents that are multiples of __3__

(only for numbers other than 0 and 1)

Question 10

What is the exception to the rule that the prime factors of a perfect cube must have exponents that are multiples of 3?

Answer 10

The perfect cubes 0 and 1

Question 11

How would you answer this?

Answer 11

60