Transcript Square Roots practice and Pythagorean Theorem

Exploring Square
Roots and the
Pythagorean Theorem
Perfect Square
A number that is a square of
an integer
2
Ex: 3 = 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
Square Root
Indicated by the
symbol
Radical Sign
Square Root
Example:
16
25
4
= 5
Square Root
Estimating square
roots of non-perfect
squares
Square Root
Find the perfect
squares immediately
greater and less than
the non-perfect
square
Square Root
Example:
32
65
The answer is between 82
which is 64
and 92
which is 81
Pythagorean
Theorem
Pythagorean
Theorem
Formula to find a
missing side of a
right triangle
Pythagorean
Theorem
ONLY WORKS
FOR RIGHT
TRIANGLES!!!
Pythagorean
Theorem
Part of a Right
Triangle:
•Hypotenuse
•2 Legs
Pythagorean
Theorem
a=
c = hypotenuse
leg
b = leg
Pythagorean
Theorem
a=
c = hypotenuse
leg
b = leg
Pythagorean
Theorem
•Lengths of the legs:
a&b
•Length of the
hypotenuse: c
Pythagorean
Theorem
The sum of the squares
of the legs is equal to
the square of the
hypotenuse
Pythagorean
Theorem
2
a
+
2
b
=
2
c
Pythagorean
Theorem
52
32
5
3
4
42
32 + 42 = 52
9 + 16 = 25
25 = 25
Pythagorean
a +b =c
Theorem
2
2
2
152 + 202 = c2
225 + 400 = c2
c
15 ft
20 ft
√625 = 25
Pythagorean
a +b =c
Theorem
6 + b = 12
2
2
2
2
2
2
36 + b2 = 144
-36
b
6 ft
-36
2
=108
b
√108 = 10.39
12 ft