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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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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