If x equals pi times y cubed and y equals the square root of 78. How would you determine the value of x?

$$\\x=\pi*y^3\qquad and \qquad y=\sqrt{78} = 78^{0.5}\\\\
then\\\\
x=\pi*(78^{(0.5)}^3)\\\\
x=\pi*78^{1.5}\\\\$$

 

$${\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{78}}}^{{\mathtt{1.5}}} = {\mathtt{2\,164.172\: \!014\: \!361\: \!556\: \!545\: \!6}}$$

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I'm not sure if you meant "(pi * y)^3" or "pi * (y^3)".

 

If you meant "x = (π*y)³":

x = (π*y)³

y = sqrt(78)

you can replace then "y" in x's equation with sqrt(78) and work from there:

x = (π * sqrt(78))³

Let's expand this out to make it easier to work with.

x = π³ * sqrt(78)³

Seeing as "sqrt(78)" is being raised to a power above 2, it's possible to simplify it further.

x = π³ * sqrt(78)² * sqrt(78)

x = π³ * 78 * sqrt(78)

There's not much left to do other than to multiply it all together.

x = 31.006 * 78 * 8.832

x = 21360

 

If you meant "x = n * (y³)":

x = π * (y³)

y = sqrt(78)

Again, let's just insert y into x's equation.

x = π * (sqrt(78))³

Again, we can simplify that square root down at least a little.

x = π * 78 * sqrt(78)

And now let's finish the equation.

x = 3.142 * 78 * 8.832

x = 2164.5