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1. 1. Presented By: Kimberly Talines Sam Sarmieto Justine Talbo Dale Kyle Sy Leenie Mae Tan Gerard Preciados
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3. 3.  Introduction: In mathematics, a square root of a number a is a number y such that y2 = a, in other words, a number y whose square (the result of multiplying the number by itself, or y × y) is a. For example, 4 and −4 are square roots of 16 because 42 = (−4)2 = 16.
4. 4.  History: The mathematical expression 'The square root of x. x - radicand √ - radical sign 2 – index
5. 5.   Finding the square root of a number is the inverse operation of squaring that number. Remember, the square of a number is that number times itself. Square Roots:
6. 6.  The Yale Babylonian Collection YBC 7289 clay tablet was created between 1800 BC and 1600 BC, showing √2 and 30√2as 1;24,51,10 and 42;25,35 base 60 numbers on a square crossed by two diagonals. The Rhind Mathematical Papyrus is a copy from 1650 BC of an even earlier work and shows how the Egyptians extracted square roots. Square Roots:
7. 7. In Ancient India, the knowledge of theoretical and applied aspects of square and square root was at least as old as theSulba Sutras, dated around 800–500 BC (possibly much earlier). A method for finding very good approximations to the square roots of 2 and 3 are given in the Baudhayana Sulba Sutra.[13] Aryabhata in the Aryabhatiya(section 2.4), has given a method for finding the square root of numbers having many digits. Square Roots:
8. 8. In the Chinese mathematical work Writings on Reckoning, written between 202 BC and 186 BC during the early Han Dynasty, the square root is approximated by using an "excess and deficiency" method, which says to "...combine the excess and deficiency as the divisor; (taking) the deficiency numerator multiplied by the excess denominator and the excess numerator times the deficiency denominator, combine them as the dividend." Square Roots:
9. 9.  Mahāvīra, a 9th-century Indian mathematician, was the first to state that square roots of negative numbers do not exist. A symbol for square roots, written as an elaborate R, was invented by Regiomontanus (1436–1476). An R was also used for Radix to indicate square roots in Giralamo Cardano's Ars Magna. Square Roots:
10. 10.  According to historian of mathematics D.E. Smith, Aryabhata's method for finding the square root was first introduced in Europe by Cataneo in 1546. The symbol '√' for the square root was first used in print in 1525 in Christoph Rudolff's Coss, which was also the first to use the then-new signs '+' and '−'. Square Roots:
11. 11.  Heron’s formula: Geometric mean: Cubic formula: Finding the volume: Quadratic formula: Formulas involving radicals:
12. 12.  In geometry, Heron's formula (sometimes called Hero's formula) is named after Hero of Alexandria[1] and states that the area of a triangle whose sides have lengths a, b, and c is, where s is the semiperimeter of the triangle; that is, Heron’s Formula:
13. 13.  In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values Geometric Mean:
14. 14.  Cubic formula:
15. 15.   The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allows the equations of motion to be solved analytically for small-angle oscillations. Pendulum: