simplifying square root radicals
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Simplifying Square Roots
Using Perfect Square Factors
Review
Square and square root – inverse operations
Ex. 1: √25 = 5, since 52 = 25 Ex. 2: √529 = 23, since 232 = 529
Terms Used with Radicals
The √ symbol is called the radical signThe root being taken (usually 2 – unwritten
– for a square root) is the indexThe number inside the radical is the
radicand
√25(2)
Perfect Square Factors
Simplify perfect square factors of the radicand
Ex. 1: √12 = √4∙3 = 2√3Ex. 2: √32 = √16∙2 = 4√2Ex. 3: 3√8 = 3√4∙2 = 3∙2√2 = 6√2
Practice Problem
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
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)
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)
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!
Solution for √18
√18 = √9 ∙2 = 3√2
Back
Solution for √27
√27 = √9 ∙3 = 3√3
Back
Solution for 2√75
2√75 = 2√25∙3 = 2∙5√3 = 10√3
Back
Solution for √98
√98 = √49 ∙2 = 7√2
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