1. Expand:

0.05361

Note: To expand shift decimal point

5.361 x 10−2

2. Simplify: 4(m3 n −2) −5 • (− 3mn4)2

Power to a Power Multiply exponents

4m−15 n10 • (−3)2m2n8

4m−15n10 • 9m2n8

Simplify

36m−15 n10 • m2n8

Multiply

36n18

Product of Powers Property

36m−13 n18

Negative Exponent Property

m13

Algebra I Concept Test # 12 – Square Roots

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8r−3t 9

Simplify:

3. (− 2r2t3)3 8r−3t 9

Power to a Power Multiply exponents

(− 2)3r6t9

8r−3t 9

− 8r6t9

r−3t 9

− 1r6t9

Simplify

Quotient of Powers Subtract exponents

− r6 – (−3)t9 – 9 − r9t0

Zero Exponent property − r9 • 1

− r9

Algebra I Concept Test # 12 – Square Roots

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:

7i = a

3i + 800 = a

3i + 800 = 7iSubstitution:

800 = 4iSubtract 3i:

200 = iDivide by 4:

200 items

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:

i = 200 items

3i + 800 = a

3(200) + 800 = aSubstitution:

600 + 800 = aSimplify:

1400 = aDivide by 4:

$ 1400.00

Algebra I Concept Test # 12 – Square Roots

5.

75 5 • 15 5 • 15

Product Property of Radicals 5 3

25 • 3 25 • 3

Simplify:

6.

81x10

Product Property of Radicals

81 • x10

9x5

3

Algebra I Concept Test # 12 – Square Roots

4

Simplify:

2

17.

64 Simplify2

18•

4

8.

32

18Reduce

16

9

Quotient Property of Radicals

16

9

Simplify

Algebra I Concept Test # 12 – Square Roots

6 • x2 • y109.

6x2y10

Product Property of Radicals

x y5 6

Simplify:

Rewrite Radicand with perfect square factor

─ 6 7

─ 3 • 2 7

2 7 ─ 3 28

2 7

Term is in simplest form, Radicand is prime

─ 3 4 • 7

2 7 Square Root

2 7

− 4 7

Multiply

Subtract

Simplify:

10.

Algebra I Concept Test # 12 – Square Roots

Algebra I Concept Test # 12 – Square Roots

11. Approximate the following square roots to the tenths place:

a) 10

**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.

Approximately 3.2

b) 79

**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.

Approximately 8.9

Algebra I Concept Test # 12 – Square Roots

12. Evaluate:

a + bc for a = 8, b = − 4, and c = − 92

Substitute(8)2 + (−4)(−9)

Exponent64 + (−4)(−9)

64 + 36

100

10

Multiply

Add

Square Root

( 3 ─ 8)5 15

13. Distribute

─ 8 5

Algebra I Concept Test # 12 – Square Roots

64 • a2 • b4

64a2b4

Simplify:

14.

8a3b • 8a−1b3

8ab2

Multiply

Product Property of radicals

Square Root

( )2

3 x = 15

7 + 3 x = 22

Solve:

15.

Isolate the radical x

Subtract

Divide

Square

3 3

– 7 – 7

x = 5( )2

x = 25

Algebra I Concept Test # 12 – Square Roots

( )2 x = 7( )2

6 x = 42

2 x + 4 x = 42

Solve:

16.

Combine like terms

Divide

Square

6 6

x = 49

17. Check your solution for #16. 2 x + 4 x = 42

Substitute

Simplify

Check Complete

2 49 + 4 49 = 42

2 • 7 + 4 • 7 = 42

14 + 28 = 42

42 = 42

Algebra I Concept Test # 12 – Square Roots

x = − 4

− 6 x = 24

5 x ─ 11 x ─ 10 = 14

Solve:

18.

Isolate the radical x

Add

Divide − 6 − 6

+ 10 + 10

Combine like terms− 6 x ─ 10 = 14

Note: The square root of a number can never be negative

No Solution

Algebra I Concept Test # 12 – Square Roots

Algebra I Concept Test # 12 – Square Roots

Note: Substitute each of the given x-coordinates into the given radical equation to find the y-coordinate.

19. Using the square root function, y = x – 7, complete the following:

y = x – 7

x y

1/4 − 6 1/2

0

1

4

− 6

− 7

− 5

a) Complete the table

b) Graph the function using the ordered pairs from part a.

123

− 1

− 5

− 4

− 3

− 2

x

y

− 5 − 1− 2− 3− 4 54321

− 7

− 6

Algebra I Concept Test # 12 – Square Roots

(49, 0)

19. Using the square root function, y = x – 7, complete the following:

c) Identify the endpoint

d) Identify the y-intercept

(0, − 7)

e) Identify the x-intercept

(0, − 7)

g) State the range y ≥ − 7

f) State the domain x ≥ 0

123

− 1

− 5

− 4

− 3

− 2

x

y

− 5 − 1− 2− 3− 4 54321

− 7

− 6

x y

1/4 − 6 1/2

0

1

4

− 6

− 7

− 5

Note: Let y = 0 and then solve for x.

0 = x – 7

7 = x

49 = x

RADICAL