Download Number 5 - Mixed Entire Radicals

Math 10C
Real Numbers: Lesson #5
Mixed and Entire Radicals
Objective: By the end of this lesson, you will be able to:
Some radicals can be written in more than one way and still have the same value. These are
called _________________________________.
Definitions:
 A radical in the form

n
b is called an _________________________________.
A radical in the form a n b is called a _________________________________.
You can “pull apart” a radical (e.g. 4  15 to 4  15 ) and get the same answer. This is called
the Multiplication Property of Radicals:
We can use this property to change some entire radicals into mixed radicals. We call this
_______________________ radicals or writing a radical in __________________ __________.
Method 1: Find a Perfect Square Factor
1. Look for a factor of the radicand that is a ________________ ____________.
* To make sure the radical is in simplest form, you must find the __________________
perfect square factor.
2. Write the radicand as a _______________ of the perfect square and its factor pair.
3. Break the radical apart at the  sign into the product of two radicals.
4. Take the _____________ _________ of the perfect square. Leave the other radical as is.
e.g. 1) Write 200 as a mixed radical in simplest form.
Math 10C
Real Numbers: Lesson #5
Method 2: Use Prime Factorization
1. Write the ____________ __________________________ of the radicand.
2. Group as many prime factors as you can into ___________.
3. Multiply ________ number from each of these pairs together. This is the number that
goes ______________ the radical.
4. The factors that don’t group into pairs stay in the __________________. Multiply these
numbers back together to get the number under the root sign.
e.g. 2) Write 54 as a mixed radical using prime factorization.
e.g. 3) The area of the square shown below is 72 cm2. Determine the length of one side as a
mixed radical in simplest form.
e.g. 4) Find the length of the missing side of the triangle. Express the answer as a mixed radical
in simplest form.
45
5
We can also simplify cube roots, fourth roots, etc. by a similar process:
 Unless you have perfect cubes, fourth powers, etc. memorized, it is probably best to use
prime factorization to simplify these.
 Instead of grouping prime factors into pairs, put them in groups equal to the __________.
Math 10C
Real Numbers: Lesson #5
e.g. 5) Write the following radicals in simplest form:
a) 3 250
b)
4
144
We can also reverse the process to convert mixed radicals to entire radicals.
e.g. 6) Write the following as entire radicals:
a) 7 10
c) 34 5
Rewriting mixed radicals as whole radicals can help order them.
e.g. 7) Without using a calculator, arrange the following radicals in order from greatest to least:
2 10 , 4 3 , 5 2 , 3 5
Check Your Understanding:
Is it possible to write every entire radical as a mixed radical? Explain why or why not.
Assignment:
p. 218-219 #9-18, 20-22