The volume of a cube can be found by multiplying the length times the width times the height of a box (V=lwh or V=s^3). If the volume of a box is 857.375 cubic inches and all of its dimensions are equal, what is the side length of the box in inches. (Round to the nearest hundredth)

Answer 1

Let's assume the side length of the box is x inches.
Since all dimensions are equal, the volume of the box is equal to x * x * x = x^3.
We know that the volume of the box is 857.375 cubic inches, so we can set up the equation x^3 = 857.375.
To solve for x, we need to take the cube root of both sides of the equation.
∛(x^3) = ∛(857.375)
x = ∛(857.375)
Using a calculator, we find that x ≈ 9.26 (rounded to two decimal places).
Therefore, the side length of the box is approximately 9.26 inches.

Answer 2

Rational or Irrational??
Check mark 40
Check mark 81
0.82
0.55555555...
Which one is rational?
1/2
Check mark 5
- . 12546987 . . .
.4451466477...

Answer 3

Rational numbers are numbers that can be expressed as the ratio of two integers.
Let's check the given numbers:

- Check mark 40: Rational. 40 can be expressed as the ratio of 40/1.
- Check mark 81: Rational. 81 can be expressed as the ratio of 81/1.
- 0.82: Rational. It can be expressed as the ratio of 41/50.
- 0.55555555...: Rational. It can be expressed as the ratio of 5/9.
- 1/2: Rational. It is already expressed as the ratio of 1/2.
- Check mark 5: Rational. 5 can be expressed as the ratio of 5/1.
- - . 12546987 . . . : Rational. It can be expressed as the ratio of -139/111.
- .4451466477...: Irrational. It is a non-repeating and non-terminating decimal.

Therefore, the numbers that are rational are:
- Check mark 40
- Check mark 81
- 0.82
- 0.55555555...
- 1/2
- Check mark 5
- - . 12546987 . . .

The number that is irrational is:
- .4451466477...

It's important to note that repeating decimals, like 0.55555555..., can also be expressed as fractions and are considered rational.