4.6-Square Roots and the Pythagorean TheoremCATHERINE CONWAY
MATH081
Perfect Square
A number that is a square of an integer
Ex: 32 = 3 · 3 = 9
3
3
Creates a Perfect Square of 9
Perfect Square
List the perfect squares for the numbers 1-12
Square Root
The inverse of the square of a number
Indicated by the symbol
Radical Sign
Square RootExample:
= 1
= 2
= 3
= 4
= 5
= 6
= 7
= 8
= 9
Practice
Simplify the following expression without using a calculator
Square RootEstimating square roots of non-perfect
squares
Find the perfect squares immediately greater and less than the non-perfect square
Example:
Approximations for the square root of 7
Pythagorean Theorem
Pythagorean Theorem
Formula to find a missing side of a right triangle
a2 + b2 = c2
ONLY WORKS FOR RIGHT TRIANGLES!!!
Pythagorean Theorem
Part of a Right Triangle:
Hypotenuse 2 Legs
a = leg
b = leg
c = hypotenuse
Pythagorean Theorem
a = leg
b = leg
c = hypotenuse
The corn
er
of the s
quare
always
points
to the h
ypoten
use
Pythagorean Theorem
Lengths of the legs: a & b Length of the hypotenuse: cThe sum of the squares of the
legs is equal to the square of the hypotenuse
a2 + b2 = c2
Pythagorean Theorem
332
42
52
4
5 32 + 42 = 52
9 + 16 = 25 25 = 25
Using the Pythagorean Theorem
Find the length of the hypothenuse, c, for the right triangle with sides, a = 6 and
b = 8
Find the length of the hypothenuse, c, for the right triangle with sides, a = 12 and b = 16a2 + b2 =
c2122 + 162 =
c2144 + 256 =
c2400 =
c2
20 = c
a2 + b2 = c2
62 + 82 = c2
36 + 64 = c2
100 = c2
10 = c