Download Square Root of a Number

Square Roots &
Pythagorean Theorem
Inverse Operations…
The opposite of + is The opposite of  is
The opposite of x2 is

Square Root of a Number:
If
2
b
= 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 a
 a 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.
8  24
2 2
OR
222
Pull out perfect squares, leave what's
left inside the radical
Estimate numbers that
aren’t perfect squares.
30
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
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.**
25
•
•
•
•
•
30
36
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.
Evaluate:
When a=1, b=-2, c=-3
b  4ac
2
 (2)  4 1 (3)
2
 4  12
 16
4
Evaluate:
1 2 3
4
1 2 3
4
At 1.12
OR
1 2 3
4
At - 0.62
PYTHAGOREAN THEOREM
Works only with right triangles
A
c
leg
b
C
2
a
+
2
b
=
2
c
hypotenuse
a
leg
B
Find the missing side using
Pythagorean Theorem.
a2 + b2 = c2
8
C
82 + 62 = c2
64 + 36 = c2
100 = c2
10 = c
6
Find the missing side using
Pythagorean Theorem.
a2 + b2 = c2
a2 + 122 = 132
a2 + 144 = 169
a2 = 25
a = 5
13
X
12
Don’t Do This!!!