Name:
Block:
Date:
Pre-Calculus 11
Sec 5.1 Working with Radicals
Objectives:
• Converting between mixed radicals and entire radicals
• Comparing and ordering radical expressions
• Identifying restrictions on the variable within a radical sign
• Simplifying radicals using addition and subtraction
Rules of Divisibility: A number is divisible by
2- when the last digit is 0, 2,4,6,8
3- when the sum of all the digits is a # divisible by 3
5- when the last digit is 0 or 5
Write in prime factorization: 12, 28, 144
Perfect Square versus not a perfect square: 25 and 10
25
2
10
Like Radicals: (same radicand and index) When adding or subtracting radicals, only like radicals can
be combined.
Pairs of like radicals
Pairs of unlike radicals
1
Restrictions on Variables:
If a radical represents a real number and has an even index, the radicand must be non-negative.
The radical 4 − x
must be greater than or equal to zero.
Mixed Radical
Entire Radicals:
Express each mixed radical in entire radical form: (don’t forget restrictions!)
Ex.1) a) 7 2
d)
4 3
Entire Radicals
Ex 2) a)
b)
a4 a
e)
j3 j
3
2
c) 5b 3b
Mixed Radicals: (restrictions!!)
200
4
b)
c9
c)
48y 5
Compare and Order Radicals:
1
4 (13) 2 , 8 3, 14, 202, 10 2
Order the radicals from least to greatest WITHOUT using a calculator!! You must convert them into
entire radicals first.
Ex. 3) Order the following radicals from least to greatest (no calculator!!)
5, 3 3, 2 6,
23
Add and Subtract Radicals:
Ex. 4) Simplify radicals and combine like terms.
a)
d)
50 + 3 2
b)
4c − 4 9c , c ≥ 0
c)
− 27 + 3 5 − 80 − 2 12
20 x − 3 45 x , x ≥ 0
Ex. 5) Consider the following designs shown for a skateboard ramp. What is the exact distance across
the base?