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```Section 4.3
Terminology
Examples :
35 ,
x
68
Examples : 3 5 ,  4 21
Part 1:
72
 36  2
6 2
1. Find the LARGEST
perfect square that is a
as a product of its
largest square and
another number.
3. Take the square root of
the perfect square and
Remember the Perfect Squares:
1, 4 , 9, 16, 25, 36, 49, 64, 81, 100…
Examples
50  5 2
25  2
150  5 6
25  6
288  12 2
144  2
48  2 12
4  12
WHOAAAAA NELLY!!!
Make sure
is in lowest
terms!
48  2 12
4 12
4
3
2 2 3
4 3
HOW COULD WE HAVE
AVOIDED THIS PROBLEM?
48  4 3
16  3
We should have written the radicand as a
product of its largest square and another
number. Not just any square! Both methods
will get you full marks, as long as your final
More mixed radicals that can be
further reduced 
6 27  6 9  3  6 3 3  18 3
4 20
 4 4  5  4 2 5  8 5
5 80  5 16  5  5 4 5  20 5
Simplifying with indices greater
than 2
3
3
4
54  27  2
3
3 2
3
16
 8 2
2 2
80
 16 5
2 5
3
4
3
4
Part 2:
3 6  9 6
 54
Try this one:
4 5  16  5
 80
1. Square the number
and write it under a
2. Multiply the two
numbers together and
More examples of mixed to entire
6 27
 36  27
 972
3
2 2
 8 2
 16
5 2
 25  2
 50
3
3
3
Try this TOUGHIE! CONVERT
FROM MIXED TO ENTIRE
How can you rewrite 6 as a 4th root??
4
6 5
 1296  5
4
4
 6480
4
Just calculate 64 (6x6x6x6) and
place it under the 4th root sign!
REMEMBER!
If you are not confident that this is the answer,
always check by evaluating both numbers in