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

Answer:

  S = √(3V/H)

Step-by-step explanation:

The opposite operation of squaring is taking the square root.

  $\boxed{S=\sqrt{\dfrac{3V}{H}}}$

_____

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:

  $\displaystyle x^\frac{1}{n}=\sqrt[n]{x}$

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

  $x^{\frac{1}{2}}=\sqrt{x}$

In the case of this problem, ...

  $(S^2)^{\frac{1}{2}}=\left(\dfrac{3V}{H}\right)^{\frac{1}{2}}\\\\S=\sqrt{\dfrac{3V}{H}}$