Associative Property of Multiplication 2
Division Theorem
Multiply Both Sides 3
Transitive Property Application 1
Substitution 10
Reorder Terms 7
Transitive Property of Equality Variation 2
Reorder Terms 8
Inverse Example
Manipulation
Add 1 to Exponent
Transitive Property Application 2
Power of 2
Power of 2 2
Transitive Property Application 4
Square Root of a Square
Square Root Example

Proof: Square Root Example

Let's prove the following theorem:

((s ⋅ s) ⋅ (1 / 4))(1 / 2) = s / 2

First, here are some examples: ((s ⋅ s) ⋅(1 / 4))(1 / 2) = s / 2

((3 ⋅ 3) ⋅ (1 / 4))^(1 / 2) = 3 / 2

((8 ⋅ 8) ⋅ (1 / 4))^(1 / 2) = 8 / 2 = 4

(8 ⋅ 125)^(1 / 2) = 125

(x + 3 ⋅ x + 3)^(1 / 2) = x + 3

Proof:

View as a tree | View dependent proofs | Try proving it

Proof Table
# Claim Reason
1 (s ⋅ s) ⋅ (1 / 4) = (s / 2) ⋅ (s / 2) (s ⋅ s) ⋅ (1 / 4) = (s / 2) ⋅ (s / 2)
2 ((s ⋅ s) ⋅ (1 / 4))(1 / 2) = ((s / 2) ⋅ (s / 2))(1 / 2) if (s ⋅ s) ⋅ (1 / 4) = (s / 2) ⋅ (s / 2), then ((s ⋅ s) ⋅ (1 / 4))(1 / 2) = ((s / 2) ⋅ (s / 2))(1 / 2)
3 ((s / 2) ⋅ (s / 2))(1 / 2) = s / 2 ((s / 2) ⋅ (s / 2))(1 / 2) = s / 2
4 ((s ⋅ s) ⋅ (1 / 4))(1 / 2) = s / 2 if ((s ⋅ s) ⋅ (1 / 4))(1 / 2) = ((s / 2) ⋅ (s / 2))(1 / 2) and ((s / 2) ⋅ (s / 2))(1 / 2) = s / 2, then ((s ⋅ s) ⋅ (1 / 4))(1 / 2) = s / 2
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