Real Numbers and The Pythagorean Theorem

A square root is a number that, when multiplied by itself, equals the given number. Every positive has a positive and negative square root.

A perfect square is a number with integers as its square root.

Being familiar with your multiplication tables will help!

You should ask, "do I know any numbers that can be multiplied by themselves to give me 49?

yes, 7 x 7 = 49

But, is there anything else that can be multiplied by itself to give us 49?

YES! -7 x -7 = 49

The radical symbol is used to represent a square root.

The number under the radical symbol is called the radicand

Like the picture says, if there is no number for the index, it is implied 2.

Right triangles typically are indicated by the square in a corner

Legs are two sides that form the right angle (a and b)

Hypotenuse is the side opposite od the right angle (c)

In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Here we have a leg (2.1cm) and the hypotenuse (2.9cm)

 $a^2+b^2=c^2$  

 $a^2+2.1^2=2.9^2$  

 $a^2+4.41=8.41$  

 $a^2=4$  

 $a=2$  our missing leg measurement is 2cm

 $8^2+15^2=c^2$  

 $64+225\ =\ c^2\ ;\ 289=c^2$  

 $17=c$  

Measurement of the hypotenuse is 17ft.

a set of three positive integers that follow the rule of

Thankfully, there is a list of Pythagorean Triples!

This list is MASSIVE and will be given to you! But you are responsible for being able to identify items on it!