1. Square Roots
Holt Algebra 1

2. Simplify each expression.
1. 62
2. 112
121 36 25 36
3. (–9)(–9) 81 4.
Write each fraction as a decimal. 2 5 5 9 5.
0.4 6.
0.5 5 3 8 –1 5 6 7.
5.375 8.
–1.83

3. A number that is multiplied by itself to form a
product is called a square root of that product.
The operations of squaring and finding a square
root are inverse operations.
The radical symbol , is used to represent square roots. Positive real numbers have two
square roots.
= 4
Positive square
root of 16
4  4 = 42 = 16
(–4)(–4) = (–4)2 = 16 –
= –4
Negative square
root of 16

4. The nonnegative square root is represented by
The nonnegative square root is represented by The negative square root is represented by – .
A perfect square is a number whose positive square root is a whole number. Some examples of perfect squares are shown in the table. 1 4 9 16 25 36 49 64 81
100 02 12 22 32 42 52 62 72 82 92
102

5. The expression does not represent
a real number because there is no real number that can be multiplied by itself to form a product of –36.
Reading Math

6. Example 1: Finding Square Roots of
Perfect Squares
Find each square root. A.
Think: What number squared equals 16?
42 = 16
Positive square root positive 4.
= 4 B.
Think: What is the opposite of the
square root of 9?
32 = 9
= –3
Negative square root negative 3.

7. Example 1C: Finding Square Roots of
Perfect Squares
Find the square root.
Think: What number squared equals ? 25 81
Positive square root positive . 5 9

8. Check It Out! Example 1
Find the square root.
1a.
22 = 4
Think: What number squared
equals 4?
= 2
Positive square root positive 2.
1b.
52 = 25
Think: What is the opposite of the square root of 25?
Negative square root negative 5.

9. The square roots of many numbers like , are not whole numbers
The square roots of many numbers like , are not whole numbers. A calculator can approximate the value of as Without a calculator, you can use square roots of perfect squares to help estimate the square roots of other numbers.

10. Example 2: Simplifying Square–Root Expressions
Simplify each expression. A.
Find a perfect square factor of 32.
Product Property of Square Roots B.
Quotient Property of Square Roots

11. Simplify each expression.
Check It Out! Example 2
Simplify each expression. A.
Find a perfect square factor of 48.
Product Property of Square Roots B.
Quotient Property of Square Roots
Simplify.

13. Example 2: Simplifying Square–Root Expressions
Simplify each expression. C.
Product Property of Square Roots D.
Quotient Property of Square Roots

14. Simplify each expression.
Check It Out! Example 2
Simplify each expression. C.
Product Property of Square Roots D.
Quotient Property of Square Roots

16. Partner activity….
Choose one……

17. HOMEWORK:
12 problem worksheet