Definition: A square root of a number is a number such that . Notation: If is a square root of a number , then we will write .

On a straight line we mark off  and . We draw a circle with the segment  as its diameter and construct the perpendicular to  through , which meets the circle in . The triangle  has a right angle at , by the theorem of elementary geometry which states that an angle inscribed in a semicircle is a right angle. Hence,  = , the right triangles  and  are similar, and we have for :

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

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