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Metamath Proof Explorer

Theorem sqrtsqi

Description: Square root of square. (Contributed by NM, 11-Aug-1999)

		Ref	Expression
	Hypothesis	sqrtthi.1	$⊢ A \in ℝ$
	Assertion	sqrtsqi	$⊢ 0 \leq A \to \sqrt{A^{2}} = A$

Step	Hyp	Ref	Expression
1		sqrtthi.1	$⊢ A \in ℝ$
2		sqrtsq	$⊢ (A \in ℝ \land 0 \leq A) \to \sqrt{A^{2}} = A$
3	1 2	mpan	$⊢ 0 \leq A \to \sqrt{A^{2}} = A$