This document provides a summary of square roots including: - The definition of a square root as a number whose square is equal to the radicand. - A brief history of square roots in ancient Babylonian, Egyptian, Indian, and Chinese mathematics, including early approximations and methods for extracting square roots. - Key figures like Aryabhata, Mahavira, Regiomontanus, and others who contributed to the development and symbolism of square roots. - Several formulas involving radicals like Heron's formula, the geometric mean, cubic formula, and the quadratic formula.

1. Presented By:
Kimberly Talines
Sam Sarmieto
Justine Talbo
Dale Kyle Sy
Leenie Mae Tan
Gerard Preciados

2. 

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. 
History:
The mathematical
expression 'The
square root of x.
x - radicand
√ - radical sign
2 – index

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. 
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. 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. 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. 
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. 
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. 
Heron’s formula:
Geometric mean:
Cubic formula:
Finding the volume:
Quadratic formula:
Formulas involving radicals:

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. 
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. 
Cubic formula:

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:

16. 
Use to solve quadratic equations.
Quadratic Formula: