Question

A certain number is both a perfect square and a perfect cube. Will its square root and its cube root always be different numbers? Explain.

Answer 1

Answer:

See below.

Step-by-step explanation:

The only  number this is true for is 1 . The square root and cube root of 1  is 1.

For all other perfect square/ perfect cube numbers they are different. For example square root of 64 is 8 and its cube root is 4.

Answer 2

A perfect square is a number whose square root is an integer; and a perfect cube is a number whose cube root is an integer.

A number that is a perfect square and perfect cube will not always have different numbers as its square root and cube root.

Perfect squares and perfect cubes between 1 and 100 are:

Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Cubes: 1, 27, 64.

The common elements are: 1 and 64

The square and cube roots of 1 and 64 are:

$\sqrt{1} = 1$

$\sqrt[3]{1} = 1$

$\sqrt{64} = 8$

$\sqrt[3]{64} = 4$

For 1, the square root and cube root are the same

For 64, the square root and cube root are different

Hence, we can conclude that:

The square root and cube root of a perfect square and perfect cube are not always different.

Read more about perfect squares and cubes at:

https://brainly.com/question/13521012