square roots & pythagorean theorem. the opposite of + is - the opposite of is the opposite of x...
DESCRIPTION
Square Root of a Number: If b 2 = a, then b is a square root of aTRANSCRIPT
Square Roots & Pythagorean
Theorem
The opposite of + is -The opposite of is The opposite of x2 is
Inverse Operations…
Square Root of a Number:
If b2 = a, then b is a square root
of a
Radical Symbol :
Radicand: number inside the radical
All positive numbers have two square roots.
POSITIVE OR NEGATIVE
a Positive square root of aa Negative square root of a
Perfect Squares:
KNOW 1-20 and their square roots.
Perfect Squares:
1,4,9,16,25,36,49,64,81,100,121, 144,169,196,225,256,289,324,
361,400
Irrational Numbers: can’t be written as a fraction
2 3
In algebra and geometry, we usually leave answers in
radical terms.
428 22
222 OR
Pull out perfect squares, leave what's left inside the
radical
Estimate numbers that aren’t perfect
squares.
is between 25 and 36 so it’s square root is
between 5 and 6. A good estimate would be about 5.5 because 5.5 squared
is 30.25
30
Better estimation:• Look for the perfect square on each
side of the number.• Find the difference from the given
number and the smaller number. **This is your numerator.**
• Find the difference between the larger number and the smaller number.**This is your denominator.**
30• 30 – 25 = 5• 36 – 25 = 11• Fraction: 5/11
• So the square root of 30 is about 5 5/11.• In a calculator, the answer comes to about
5.477225.• So we were very close.
25 36
Evaluate: acb 42
When a=1, b=-2, c=-3
2
124
16
4
)3(14)2(
Evaluate:
4321
4321 OR
4321
At 1.12 At - 0.62
PYTHAGOREAN THEOREM
Works only with right triangles
a2 + b2 = c2
hypotenuse
leg
leg
A
b
C a B
c
Find the missing side using Pythagorean
Theorem.
8
6
C
a2 + b2 = c2
82 + 62 = c2
64 + 36 = c2
100 = c2
10 = c
12
13
X
Find the missing side using Pythagorean Theorem.
a2 + b2 = c2
a2 + 122 = 132
a2 + 144 = 169a2 = 25a = 5
Don’t Do This!!!