The document discusses square roots and the Pythagorean theorem. It defines square roots, their notation, and provides examples of calculating positive and negative square roots. It then gives a brief history of Pythagoras, noting that he was a Greek mathematician born in 570 BCE who studied in Egypt and made many contributions to mathematics, including proving what is now known as the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

1. Square root and
Pythagoras Theorem
1. Square root
2. History & Definition of
Pythagoras theorem
3. Example
Sheri Davis
MATH 114
February 2018

2. Pythagoras Theorem

3. Square Root and
The Pythagoras Theorem
Finding a square root of a number is the inverse operation
of squaring a number.
This symbol is the radical or the radical sign
n
a
index
radical sign
radicand
The expression under the radical sign is the radicand.
The index defines the root to be taken.

4. This symbol represents the negative square root of a
number.
The above symbol represents the positive or principal
square root of a number.
−
Square Root and
The Pythagoras Theorem

5. If a is a positive number, then
a is the positive square root of a and
100 =
a− is the negative square root of a.
A square root of any positive number has two roots – one
is positive and the other is negative.
Examples:
10
25
49
=
5
7
36− = 6−
9− = non-real #
=169 13
Square Root and
The Pythagoras Theorem
=0 0

7. History of Pythagoras
• Pythagoras was born in Samos, Greece around 570 BCE
• He is often described as the first pure mathematician.
• Around 535 BCE, Pythagoras journeyed to Egypt to learn
more about mathematics and astronomy
• Pythagoras made many contributions to the world of
math including:
• Studies with even/odd numbers
• Studies involving Perfect and Prime Numbers
• Irrational Numbers
• Various theorems/ideas about triangles, parallel lines,
circles, etc.
• Of course THE PYTHAGOREAN THEOREM

9. The Theorem

14. THE END
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