Download Objective # 43 Square Roots and Operations with Radicals Material

Objective # 43
Material:
Square Roots and Operations with Radicals
Teacher Notes
Homework: worksheet
Parts of a Radical:
Square Root:
is a radical operation (index = 2) performed on a number to get a value, such that the
value when squared will give the original number back.
Cube Root:
is a radical operation (index = 3) performed on a number to get a value, such that the
value when cubed will give the original number back.
Example:
Perform the following operations:
a)
=6
b)
Simplest Form of a Square Root:
Perfect Squares:
Example:
a)
=8
c)
d=) 13
= 2 e)
A square root is in its simplest form when the radicand does NOT
contain a factor which is a perfect square.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, etc.
Simplify each of the following:
is not in its simplest form because 50 has a factor of 25 which is a perfect square
b)
c)
d)
e)
f)
g)
NOW DO EXERCISE 1 ON THE WORKSHEET!
=3
Multiplying and Dividing Square Roots:
Example:
If two square roots are being multiplied or divided, then write a
single square root and move the multiplication or division inside
that square root.
Perform the following operations and simplify all radicals:
a)
b)
c)
d)
NOW DO EXERCISE 2 ON THE WORKSHEET!
Like Square Roots:
Examples:
Like Square Roots are square roots that have the same number inside the radical sign.
Like Square Roots:
NOT Like Square Roots:
Adding and Subtracting Square Roots:
Example:
ONLY like square roots can be added or subtracted ... carry the
common square root and add or subtract the coefficients
(Numbers in front of the square root)
Perform the following operations and simplify all radicals:
a)
b)
NOTE:
These are not like square roots and can’t be added but they can be simplified
Once they are simplified we notice that they a r e now like square
roots and can now be added
c)
NOW DO EXERCISE 3 and 4 ON THE WORKSHEET!
d)
Square Roots and Operations with Radicals
Worksheet
1.
Express each of the following radicals in their simplest form:
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
2.
Perform the following operations and simplify all radicals:
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
3.
Perform the following operations and simplify all radicals:
a)
b)
d)
c)
e)
f)
g)
I)
h)
g)
h)
4.
Perform the following operations and simplify all radicals:
a)
b)
c)
d)
e)