Square root of a real number
Square root
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 .
Construction of the square root of a real number using straight ruler and compass
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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References
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.
Applet
Write the number whose square root you want to find. Next use the slider to animate the construction.