If we square a number and then take the square root of the result, then the output is the original number. Here are some examples:

High-Level Proof

(x⋅x) = x^{2, so x⋅x^1/2 = x21/2}

We claim that

x^{21/2 = x(2 ⋅ 1/2)}

2 ⋅ 1/2 is 1, so x^{(2 ⋅ 1/2) == x}

Quiz (1 point)

• x ⋅ x = x²
• (x^m)ⁿ = x^{(m ⋅ n)}
• 2 ⋅ (1 / 2) = 1
• x¹ = x

• if x ⋅ x = x², then (x ⋅ x)^{(1 / 2)} = (x²)^{(1 / 2)}

• if 2 ⋅ (1 / 2) = 1, then x^{(2 ⋅ (1 / 2))} = x¹

• if the following are true:

  • a = b
  • b = c
  • c = d
  • d = e

  then a = e

Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.

Step	Claim	Reason (optional)	Error Message (if any)
1
2
3
4
5
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9
10

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