Download Chapter 11 Square Roots, Pythagorean Theorem

Chapter 11
Notes 11-1
Square Roots and Irrational Numbers
perfect square – the answer when a number multiplied by itself
example 3 x 3 = 9
9 is a perfect square
square root – the number that when multiplied by itself equals the given number
.
the square root of 100 is 10
example 100 = 10
rational number – ratio, fraction – this is a number that can be written as a fraction
including terminating decimals, and repeating decimals
¼ = 0.25
⅓ = 0.333333 = 0.3
examples
irrational number – the square root of a non perfect square
a number that can not be written as a fraction
examples 10
or
= 3.141592538979323846264338327950288…

To find the square root of a number that is NOT a perfect square, just find the square root of a perfect
so 10 = 3
square that is CLOSE to the non-perfect square
9 = 3
Notes 11-2
Pythagorean Theorem
hypotenuse – the longest side of a right triangle – it is opposite the right angle
leg – a shorter side of a right triangle
2
2
2
Pythagorean Theorem – a + b = c
The sum of the squares of the legs is equal to the square of the hypotenuse.
example
32 + 42 = 52
102 + 112 ?= 122
9 + 16 = 25
100 + 121 ?= 144
25 = 25 yes
221 ≠ 144 no
If given a leg, and the hypotenuse, to solve for the missing side, plug in and solve.
If the hypotenuse is 5 and one side is 4, what is the remaining side?
example a2 + 42 = 52
a2 + 16 = 25
– 16
– 16
2
a = 9
a2
=
a = 3
9