Question

Make r the subject of this formula
v=3 cubed (square root p+ r)

Answer 1

`\displaystyle r=(v^2 )/(3^(6) )-p`

Explanation:

`v=3^3(√(p+r) )`

Divide both sides by 3³.

`(v)/(3^3 ) =(3^3(√(p+r) ))/(3^3)`

`(v)/(3^3 ) =√(p+r)`

Square both sides.

`((v)/(3^3 )) ^2 =(√(p+r))^2`

`(v^2 )/(3^(3 * 2) )=(√(p+r))^2`

`(v^2 )/(3^(6) )=p+r`

Subtract p from both sides.

`(v^2 )/(3^(6) )-p=p+r-p`

`(v^2 )/(3^(6) )-p=r`

Switch sides.

`r=(v^2 )/(3^(6) )-p`

Answer 2

`r = {((v)/(27) ) } ^(2) \: - p`

Explanation:

`v = {3}^(3) √(p + r) \\ v = 27 √(p + r) \\ (v)/(27) = (27 √(p + r) )/(27) \\`

`(v)/(27) = √(p + r) \\ {((v)/(27) ) }^(2) = p + r \\ {((v)/(27) ) } ^(2) \: - p = r \\`