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Simplifying Square Roots





 

Videos and solutions to help Grade 8 students learn how to use factors of a number to simplify a square root.

New York State Common Core Math Grade 8, Module 7, Lesson 4

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Lesson Plans and Worksheets for Grade 8

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More Lessons for Grade 8

Common Core For Grade 8

Lesson 4 Student Outcomes

• Students use factors of a number to simplify a square root.

Lesson 4 Summary

Square roots of non-perfect squares can be simplified by using the factors of the number. Any perfect square factors of a number can be simplified.

Lesson 4 Classwork

1. a. What does \(\sqrt {16} \) equal?
b. What does equal? 4 x 4 equal?
c. Does \(\sqrt {16} \) = \(\sqrt {4 \times 4} \) ?
2. a. What does \(\sqrt {36} \) equal?
b. What does equal? 6 x 6 equal?
c. Does \(\sqrt {36} \) = \(\sqrt {6 \times 6} \) ?
3. a. What does \(\sqrt {121} \) equal?
b. What does equal? 11 x 11 equal?
c. Does \(\sqrt {121} \) = \(\sqrt {11 \times 11} \) ?
4. a. What does \(\sqrt {81} \) equal?
b. What does equal? 9 x 9 equal?
c. Does \(\sqrt {81} \) = \(\sqrt {9 \times 9} \) ?
5. What is another way to write \(\sqrt {20} \) ?
6. What is another way to write \(\sqrt {28} \) ?

Example 1
Simplify the square root as much as possible.
\(\sqrt {50} \) =

Example 2
Simplify the square root as much as possible.
\(\sqrt {28} \) =

Exercises 7–10
Simplify the square roots as much as possible.
Example 3
Simplify the square root as much as possible.
\(\sqrt {128} \) =

Example 4
Simplify the square root as much as possible.
\(\sqrt {288} \) =
Exercises 11–14



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