This document discusses simplifying square roots by using perfect square factors. It explains that a square root can be simplified by factoring the radicand into perfect square factors. Examples are provided of simplifying square roots of 12, 32, and 48 in this way. The document then provides practice problems for simplifying the square roots of 18, 27, 75, and 98 and includes the solutions.

1. Simplifying Square Roots
Using Perfect Square Factors

2. Review
Square and square root – inverse
operations

Ex. 1: √25 = 5, since 52 = 25

 Ex. 2: √529 = 23, since 232 = 529

3. Terms Used with Radicals
(2)
√25
The √ symbol is called the radical sign

 The root being taken (usually 2 – unwritten
– for a square root) is the index
The number inside the radical is the
radicand


4. ect square fact
= √4∙3 = 2√3
or
√16∙2 = 4√2
3√4∙2 = 3∙2√2 = 6√
Perfect Square Factors
Simplify perf
radicand
s of the
Ex.
Ex.
Ex.
1:
2:
3:
√12



√32 =
3√8 = 2

5. Practice 1
Now try this Problem: Simplify √48

Solution:
√48 = √16∙3 = 4√3

OR:
√48 = √4∙12 = 2√12 = 2√4∙3 = 2∙2√3 = 4√3


6. Now Try These
Hint: Look for factors of 4, 9, 25, or 49
1. Simplify √18
2. Simplify √27
3. Simplify 2√75
4. Simplify √98
(answers on the next slide)

7. Answers to previous problems
1. √18 = 3√2 (click here to see the solution)
2. √27 = 3√3 (click here to see the solution)
3. 2√75 = 10√3 (click here to see the solution)
4. √98 = 7√2 (click here to see the solution)

8. The End
Did you miss any of the previous
problems? If so, try them again.
Then continue with the next content item
of the lesson!

9. Solution for √18
√18 = √9 ∙2 = 3√2
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10. Solution for √27
√27 = √9 ∙3 = 3√3
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11. Solution for 2√75
2√75= 2√25∙3= 2∙5√3= 10√3
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12. Solution for √98
√98 = √49 ∙2 = 7√2
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