Name
10A – Simplifying Radicals
You will watch a video/take notes on the following examples. Then you need to do the practice on your own.
2 OPTIONS on how to simplify square roots:
1. For All Radicals, make a factor tree. For EVERY TWO of a factor you can bring ONE out. It is a TWO for ONE deal. In other words, if they have a friend,
they can come out, if they do not, they need to stay inside the radical.
2. Find all perfect square factors (4, 9, 16, 25, etc.). Then you can take the squares of those factors and bring them outside the radical. If it is not a perfect
square, it needs to stay inside the radical. Always check to make sure you have pulled out ALL perfect squares!
Cube Roots:
1. You need to find a number that is multiplied not just one time by itself, but two times.
2. You can have a cube root of a negative number…. The cube root of -8 is -2 because (-2)(-2)(-2) = -8
Simplifying variable:
1. If you have a square root, then you divide the exponent of the variables by two. If you have an even numbered exponent, all of the variables will come
out of the radical. If you have an odd numbered exponent, you will still have one variable left under the radical.
2. If you have a root greater than two, you simply divide by that root. You will see this a great deal in Algebra II.
Video Example
Try on Your Own (answer will be in video)
Bring to class completed (do on your own)
What number is equal to
What is the value of
1
What is the value of
2
?
Find two consecutive whole numbers that
lies between.
?
Find two consecutive whole numbers that
lies between.
?
Find two consecutive whole numbers that
lies between.
3
Simplify.
Simplify
Simplify
4
Find the value of
.
Find the value of
.
Find the value of
.
1
5
Simplify.
Simplify
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
6
7
8
8
2
10B Adding, Subtracting, Multiplying Radicals
Adding/Subtracting Radicals:
1. Simplify each individual term.
2. Then combine like terms. You must have the exact same radical in order to add/subtract radicals. Treat it like a
variable.
Multiplying Radicals:
1. Simplify each individual term.
2. Multiply the numbers OUTSIDE of the radical.
3. Multiply the numbers on the INSIDE of the radical. You may want to just keep them as factors to help you with your
factor tree.
4. Simplify the inside of the radical. Make sure that no perfect squares are still under the radical.
1
Video Example
Video Example
Try on your OWN (bring answers tomorrow)
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
2
3
3
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
4
5
4
10C – Rationalizing the Denominator
You should NOT leave any radicals in the denominator!!!!!!
1. If you have a monomial in the denominator and numerator, you need to:
a. Simplify the fraction first. You can simplify inside with inside and outside with outside.
b. Multiply the fraction by “one” (you multiply both numerator and denominator by the radical in the denominator)
c. Simplify the fraction.
2. If you have a binomial in the denominator, you need to:
a. Multiply the fraction by “one” (you multiply both the numerator and denominator by the conjugate of the denominator)
b. Simplify both the numerator and denominator.
c. You should NOT have a radical in the denominator after simplifying.
Video Example
Video Example
Try on your OWN (bring answers to class)
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
1
2
5
3
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
Simplify.
4
10D – Radical Equations
One Radical:
1.
Isolate the RADICAL.
2.
Square both sides.
3.
Solve for the variable.
4.
Check that the solution or solutions are valid.
Two Radicals:
1. Square both sides.
2. Solve for the variable.
6
3. Check that the solution or solutions are valid.
1
2
3
4
Video Example
Try on your OWN (answer will be in video)
Bring to class completed (do on your own)
Solve:
Solve:
Solve:
Solve:
Solve:
Solve:
Solve:
Solve:
Solve:
Solve:
Solve:
Solve:
7
8
10E – Pythagorean Theorem, Distance Formula, Mid-Point Formula
Pythagorean Theorem:
Distance Formula:
Ex. 1
Mid-Point Formula:
Ex. 2
Your Turn
Solve for X.
Find the distance
between:
and
Find the Mid-point
=
and
Find the Mid-point
=
=
and
=
Find the Mid-point
=
and
=
9