Proof: Square Root Example

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(s ⋅ s) ⋅ (1 / 4) = (s / 2) ⋅ (s / 2)	(s ⋅ s) ⋅ (1 / 4) = (s / 2) ⋅ (s / 2) (manipulation)
2	square root of ((s ⋅ s) ⋅ (1 / 4)) = square root of ((s / 2) ⋅ (s / 2))	if (s ⋅ s) ⋅ (1 / 4) = (s / 2) ⋅ (s / 2), then square root of ((s ⋅ s) ⋅ (1 / 4)) = square root of ((s / 2) ⋅ (s / 2)) (Substitution)
3	square root of ((s / 2) ⋅ (s / 2)) = s / 2	square root of ((s / 2) ⋅ (s / 2)) = s / 2 (Square Root Property)
4	square root of ((s ⋅ s) ⋅ (1 / 4)) = s / 2	if square root of ((s ⋅ s) ⋅ (1 / 4)) = square root of ((s / 2) ⋅ (s / 2)) and square root of ((s / 2) ⋅ (s / 2)) = s / 2, then square root of ((s ⋅ s) ⋅ (1 / 4)) = s / 2 (Transitive Property of Equality)

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