1. Algebra I Concept Test # 12 – Square Roots
1. Expand:
x 10−2
Note: To expand shift decimal point
2. Simplify: (m3 n −2) −5 • (− 3mn4)2
4m−15 n10 • (−3)2m2n8
4m−15n10 • 9m2n8
Power to a Power  Multiply exponents
Simplify
36m−15 n10 • m2n8
Multiply
Product of Powers Property
36m−13 n18
Negative Exponent Property
36n18
m13
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2. Algebra I Concept Test # 12 – Square Roots
Simplify:
3. (− 2r2t3)3
(− 2)3r6t9
8r−3t 9
8r−3t 9
Power to a Power  Multiply exponents
− 8r6t9
− 1r6t9
Simplify
8r−3t 9
r−3t 9
− r6 – (−3)t9 – 9
− r9t0
Quotient of Powers Subtract exponents
− r9 • 1
Zero Exponent property
− r9

3. Algebra I Concept Test # 12 – Square Roots
4. The Euler Company has fixed costs of $800 per week. Each item produced by the company costs $3 to manufacture and can be sold for $7.
a) How many items must be produced to reach the
break-even point (Income = Cost)?
Let, a = dollar amount
i = number of items
Write two Equations:
3i = a
7i = a
Substitution:
3i = 7i
Subtract 3i:
800 = 4i
Divide by 4:
200 = i
200 items

4. Algebra I Concept Test # 12 – Square Roots
4. The Euler Company has fixed costs of $800 per week. Each item produced by the company costs $3 to manufacture and can be sold for $7.
b) How much does the company have to make to
break-even?
Let, a = dollar amount
i = number of items
Equations:
3i = a
i = 200 items
Substitution:
3(200) = a
Simplify:
= a
Divide by 4:
1400 = a $

5. Algebra I Concept Test # 12 – Square Roots
Simplify: 5.
5 •
5 • 15 75
25 • 3
25 •
Product Property of Radicals 6.
81x10
81 • x10
Product Property of Radicals
9x5

6. Algebra I Concept Test # 12 – Square Roots
Simplify: 1 1 7. 64 • 8
Simplify 2 2 4 8. 18 9 9
Reduce 32 16 16
Quotient Property of Radicals 3
Simplify 4

7. Algebra I Concept Test # 12 – Square Roots
Simplify: 9.
6x2y10
6 • x2 • y10
Product Property of Radicals
x y5 6

8. Algebra I Concept Test # 12 – Square Roots
Simplify:
10. ─
Rewrite Radicand with perfect square factor
Term is in simplest form, Radicand is prime
─ • 7
─ 3 •
Square Root ─
Multiply −
Subtract

9. Algebra I Concept Test # 12 – Square Roots
11. Approximate the following square roots to the tenths place:
a) 10
Approximately 3.2
**Notice the square root of 9 is 3 and the square
root of 16 is 4.
Since 10 is between 9 and 16, the square root of 10
must be between 3 and 4.
b) 79
Approximately 8.9
**Notice the square root of 64 is 8 and the square
root of 81 is 9.
Since 79 is between 64 and 81, the square root of 79
must be between 8 and 9.

10. Algebra I Concept Test # 12 – Square Roots
12. Evaluate:
a + bc for a = 8, b = − 4, and c = − 9 2
Substitute
(8)2 + (−4)(−9)
64 + (−4)(−9)
Exponent
Multiply
100
Add 10
Square Root

11. Algebra I Concept Test # 12 – Square Roots
13. Distribute
( ─ 8) 5 15 ─
Simplify:
14.
8a3b
• a−1b3
64a2b4
Multiply
64 • a2 • b4
Product Property of radicals
8ab2
Square Root

12. Algebra I Concept Test # 12 – Square Roots
Solve:
15.
x = 22
Isolate the radical x
– 7
– 7
Subtract
3 x = 15
Divide 3 3
( )2
( )2
x = 5
Square
x = 25

13. Algebra I Concept Test # 12 – Square Roots
Solve:
Combine like terms
16.
2 x x = 42
6 x = 42
Divide 6 6
( )2
( )2
x = 7
Square
x = 49
17. Check your solution for #16.
2 x x = 42
= 42
Substitute
2 • • 7 = 42
Simplify
= 42
42 = 42
Check Complete

14. Algebra I Concept Test # 12 – Square Roots
Solve:
18.
5 x ─ x ─ = 14
Isolate the radical x
− x ─ = 14
Combine like terms
+ 10
+ 10
Add
− 6 x =
Divide
− 6
− 6
x = − 4
Note: The square root of a number can never be negative
No Solution

15. Algebra I Concept Test # 12 – Square Roots
19. Using the square root function, y = x – 7, complete the following:
y = x – 7
a) Complete the table
b) Graph the function using the
ordered pairs from part a.
Note: Substitute each of the given
x-coordinates into the given
radical equation to find the
y-coordinate. x y 4
− 5 1 2 3
− 1
− 5
− 4
− 3
− 2 x y 5 4
− 7
− 6 1
− 6
1/4
− 6 1/2
− 7

16. Algebra I Concept Test # 12 – Square Roots
19. Using the square root function, y = x – 7, complete the following:
RADICAL
c) Identify the endpoint
(0, − 7)
d) Identify the y-intercept
(0, − 7)
e) Identify the x-intercept
(49, 0)
f) State the domain
x ≥ 0 x y
g) State the range
y ≥ − 7 4
− 5 1 2 3
− 1
− 5
− 4
− 3
− 2 x y 5 4
− 7
− 6
Note: Let y = 0 and
then solve for x. 1
− 6
1/4
− 6 1/2
0 = x – 7
− 7
7 = x
49 = x