May 11 & 12, 2015
9.4 Simplifying Radicals
Try:
1
?
1
1
*Use the
Pythagorean Thm.
?
1
1
1
Properties of Radicals
1) Product Property
√a·b = √a ·√b where a ≥ 0 and b ≥ 0
2) Quotient Property
√a where a ≥ 0 and b > 0
a
=
b √b
Ex: √4· 25
Ex:
4
25
When asked to "simplify expressions" put into....
Simplest Form
➙ no perfect square factors
➙ no fractions in the radicand
➙ no radicals in the denominator
Ex: Simplify.
1) √48
2)
3) √18
3
7
16
4) 80
45
MORE...
5) 2
5
4
6) 5
6
2
7) 1 √32· √2
2
8) √7 · √18
√2
May 11 & 12, 2015
9.5 Pythagorean Theorem and Its Converse
A
Pythagorean Theorem
Always longest side!
In a right triangle, the square of the
length of the hypotenuse is equal to
legs
the sum of the squares of the lengths
of the legs,
OR
a2 + b2 = c2
c = hypotenuse
b
C
a
B
Khan Academy (2nd video)... pythagorean-theorem-2.webloc
A little history... http://www.youtube.com/watch?v=8R8b4NelWN4
Take a look at this proof... http://www.mathsisfun.com/pythagoras.html
Ex1: Find c, if a=4 and b=3.
Ex2: Find a, if b = 2 and c = 8.
Converse of Pythagorean Theorem
If a2+b2=c2 , then the triangle is a right triangle.
Ex3: Determine whether the given lengths are sides of a right
triangle. Remember c has to be the longest side!
a) 15, 20, 25
b) 13, 8, 10