[b][br]Definition:[/b] A square root of a number [math]x[/math] is a number [math]r[/math] such that [math]r^2=x[/math].[br][b][br]Notation:[/b] If [math]r[/math] is a square root of a number [math]x[/math], then we will write [math]r=\sqrt{x}[/math].[br]

On a straight line we mark off [i][math]OA=a[/math] [/i]and [math]AB=1[/math]. We draw a circle with the segment [i][math]OB[/math][/i] as its diameter and construct the perpendicular to [i][math]OB[/math][/i] through [i][math]A[/math][/i], which meets the circle in [i][math]C[/math][/i]. The triangle [i][math]OBC[/math][/i] has a right angle at [i][math]C[/math][/i], by the theorem of elementary geometry which states that an angle inscribed in a semicircle is a right angle. Hence, [math]\angle OCA[/math] = [math]\angle ABC[/math], the right triangles [i][math]OAC[/math][/i] and [i][math]CAB[/math][/i] are similar, and we have for [i][math]x=AC[/math][/i]:[br][br][center][math]\frac{a}{x}=\frac{x}{1}[/math][br][math]x^2=a[/math][br][math]x=\sqrt{a}[/math].[/center]

Courant, R., Courant, R., Robbins, H., Stewart, I., Courant, R., Courant, R., Robbins, H., & Robbins, H. (1996).[br][i]What is mathematics?: an elementary approach to ideas and methods[/i]. Oxford University Press.[br][br][i]Square Root[/i]. from Wolfram MathWorld. (n.d.). https://mathworld.wolfram.com/SquareRoot.html.[br]

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