Aim #4: How do we simplify radicals?
Homework: Handout
9-13-16
Do Now: State whether the following numbers are rational or irrational. Then evaluate and
round to the nearest tenth, if necessary.
a.
b.
c.
What is the difference between a rational and irrational number?
a
Rational Number: A number that can be expressed as a fraction in the form /b
where a and b are integers and b ≠ 0 ; all terminating and repeating decimals.
Irrational Number: A number that cannot be expressed as a fraction. Nonterminating, non-repeating decimals.
Simplifying Radicals:
index
√
radicand
Example:
radical
The radicand is the number under the radical sign. The index represents the root
you are taking. The index is assumed to be 2 (taking the square root) if nothing is
written.
A radical is in simplest form when:
-No radicands have perfect square factors other than 1.
-No radicands contain fractions.
-No radicals appear in the denominator of a fraction.
To simplify: find the largest perfect square which will divide evenly into the
number under your radical sign.
perfect squares:
Homework: Finish Aim #3b
2
2
13) 3a + 2a + 1
2
2
3
2
16) 16a - 64b
17) -20a + 11
18) x - 2x - 8x
b+1
2
2) x
7)
8) 15a b c
3
2
2
20) x + x - 42
3
22)
1) y
2
15) a + 2ab + b
19) -6b - 26b + 14b
21) x + 5
2
14) 4a - 5a + 4
2
23) 10a + 5ab - 6a b - 3b
3) 16y
3 5 10
2b
9)
4)
2
5)
6)
10)
11) 2ab
2
24) -a + 2
13
12) -12x
7
9.
10.
11.
12.
Simplify each radical expression.
36
Sum It Up!
When simplifying radicals we first look for perfect square factors and exponents
that are divisible by the index. Then the remaining factors are left under the
given root.