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