1. Warm Up
Simplify. 25 64
144
225
5. 202
400

2. Think about the relationship between the area of a square and the length of one of its sides.
area = 36 square units
side length = = 6 units
Square root: A number that when multiplied by itself, forms a product.
Taking the square root of a number is the inverse of squaring the number.
62 = = 6

3. Every positive number has two square roots, one positive and one negative.
principle square root: non-negative square root.
Principle square root
Negative square root -
perfect square: a number that has integers as its square roots.
Ex: 1, 4, 9, 25, 64, 81
Caution!

4. Example 1: Positive and Negative Square Roots
Find the two square roots of each number.
A. 49
D. 25
25 = 5
49 = 7
25 = –5 –
49 = –7 –
B. 100
E. 144
100 = 10
144 = 12
100 = –10 –
144 = –12 –
C. 225
F. 289
289 = 17
225 = 15
289 = –17 –
225 = –15 –

5. Example 2: Application
A square window has an area of 169 square inches. How wide is the window? 13
Use the positive square root; a negative length has no meaning. The window is 13 inches wide.
The area of a square is s2, where s is the length of a side.
Remember!

6. Check It Out: Example 2
A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening?
Write and solve an equation to find the area of the kitchen table
16 = 4
Use the positive square root; a negative length has no meaning. So the table is 4 feet wide, which is less than 5 feet, so it will fit through the van door.

7. Example 3: Evaluating Expressions Involving Square Roots
Simplify the expression.
3 4 A B
= 3(6) + 7
3 4 =
1.5625 =
3 4
= 25 =
= 2

8. Check It Out: Example 3
Simplify the expression. t2
1 4 + A B.
= 2(5) + 4
1 4 = 9 =
1 4
= 3 +
= 14
1 4
= 3

9. Lesson Quiz
Find the two square roots of each number.
Evaluate each expression.
– 2 49 9
50 13 7
5. Ms. Estefan wants to put a fence around 3 sides of a square garden that has an area of 225 ft2. How much fencing does she need?
45 ft