9.3a Simplifying Radicals
Algebra 1
Simplifying Radicals
When we find the square root of a number that is not a perfect square, we write the
number in simplified radical form. A radical is in simplified radical form if there is
neither a perfect square factor under the radical or a fraction.
Recall:
I. Model Problems
In this example we will practice simplifying a radical.
Example 1:
Write the number under the radicand as a product of
perfect squares.
Write as product of radicals.
Find square roots.
Simplify.
Answer:
Just a reminder: When we are given
we want the principal, or positive root. Not the positive and
. If both the
negative. If the negative root is desired, the problem would be given in this form:
.
positive and negative root are desired, the problem would be given in this form:
In this example we will practice simplifying a radical using a factor tree to find perfect
squares.
Example 2:
First factor.
Every pair of prime factors
is a perfect square.
Simplify.
Answer:
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II. Practice Problems
Simplify.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. 4 18
14. 3 8
15. 5 27
16. 7 12
17. 7 32
18. 3 40
19. 11 72
20. 9 242
III. Challenge Problems
Reverse the process. Un-simplify the simplified radical form.
Write as one number under the radicand.
21.
22.
23.
24. Find the mistake in the student’s work.
25. Given that a and b are positive write
in simplified radical form.
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IV. Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. 4 18 = 4 9 2  12 2
14. 3 8 = 3 4 2  6 2
15. 5 27 = 5 9 3  15 3
16. 7 12  7 4 3  14 3
17. 7 32  7 16 2  28 2
18. 3 40  3 4 10  12 10
19. 11 72  11 36 2  66 2
20. 9 242  9 121 2  99 2
21.
22.
23.
24. Missed a perfect square.
25.
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