Download Simplifying Radicals: When you are simplifying square roots, look for

Algebra II
5-6 D1 Notes – SIMPLIFYING RADICALS
Target Goals:
1. Simplify radical expressions
2. Add, subtract, multiply and divide radical expressions
Background information: In order to completely factor a number, we can use prime factorization
(remember factor trees!?). Let’s try to factor 84. Then find
84 .
What about a faster way? We can look for perfect squares. This will help you break down numbers
faster. When you look at a number, try to find the HIGHEST perfect square the number holds. Can you
list the perfect squares 1-100?
Let’s try to factor 180 using perfect squares. Then find
180 .
Simplifying Radicals: When you are simplifying square roots, look for perfect squares.
1)
294
2)
525
3)
7500
When you are simplifying roots with an index other than two, your objective will change. For
instance, with a cube root, you need to look for a perfect cube that goes in to the radicand.
5
3) 3 40
4) 4 16
5) 96
Let’s try some examples with variables. When we try variable examples, we have to ask ourselves the
question, “How many times does the index go into the exponent beneath the radical sign”. The remainder
gets stuck under the radical sign.
5) 3 x 7
6)
4
x10
7)
y 32
8)
6
x32 y 6
32a3
10) 64a 2b3c
9)
11)
5
3
12)
54a3b7
4
32x8 y 6
13) Which of the following is NOT a length of a side of the following right triangle?
a)
2
6
8
b)
2 2
c)
42
d)
4 2