Question

What is the opposite operation of squaring? Using this opposite operation, rewrite the equation S² = 3V / H so s is by itself on one side of the equation.

Step by step answer like this:
V=1/3 HS²
Solving for S².
Multiply both sides by 3.
3V= 3 x 1/3 HS²
3V=HS²
Divide both sides by H.
3V/H=HS²/H
3V/H=S²
Switch sides
S²=3V/H

Answer 1

S = √(3V/H)

Explanation:

The opposite operation of squaring is taking the square root.

`\boxed{S=\sqrt{(3V)/(H)}}`

_____

In the more general sense, the inverse operation for raising to a power is raising to the reciprocal of that power. We know that ...

(a^b)^c = a^(bc)

When we want bc=1, we must have c=1/b.

We know that the denominator of a fractional power is the index of the corresponding root:

`\displaystyle x^(1)/(n)=\sqrt[n]{x}`

For n=2, we don't usually write the index in the root symbol:

`x^{(1)/(2)}=√(x)`

In the case of this problem, ...

`(S^2)^{(1)/(2)}=\left((3V)/(H)\right)^{(1)/(2)}\\\\S=\sqrt{(3V)/(H)}`