Basic Skills Assignments



Algebra 1CC Name

L1-Notes: Simplifying Radicals

Simplifying Radical Expressions

Radical Expression: an expression that contains a square root.

Example: [pic]

Radicand: the expression under the radical sign.

The radicand is in simplest form if it contains no perfect squares.

Perfect Squares: a number squared.

Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121…

Simplifying Radicals

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] (reduce first) 6. [pic]

7. [pic] same as [pic] 8. [pic] 9. [pic]

10. ( [pic] 11. [pic] 12. [pic]

Square Roots of Variables

RULES:

Even powers: Divide by 2.

Odd Powers: Leave one and then divide by 2.

Evens:

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

Odds:

7. [pic] 8. [pic] 9. [pic]

Practice

Simplify.

10. [pic] 11. [pic]

12. [pic] 13. [pic]

14. [pic] 15. [pic]

16. [pic] 17. [pic]

Radical Review

Simplify.

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

7. [pic] 8. [pic] 9. 2[pic]

Day 5

Sec 11-2: + and – Radical Expressions

Simplify.

1. 12x + 3 – 5x 2. 2[pic] + 7[pic] – [pic]

Combine Like Terms

* Add coefficients

*Radical stays the same

3. 6[pic] – 2[pic] – 5[pic] 4. 7[pic] + 8[pic] – 4[pic] – [pic]

5. 3[pic] – [pic] 6. 6[pic] – 8[pic] + 2[pic]

HW: Worksheet #5

Day 6

Products and Conjugates

Multiply

1. [pic]([pic]+4[pic]) 2. (4[pic]–2[pic])(3[pic]–[pic])

3. [pic] 4. [pic]

5. Find Perimeter and Area of the Rectangle.

Width: 4[pic] – 2[pic]

Length: 5[pic] + 7[pic]

Conjugates: rationalize the denominator with addition and subtraction of radicals. Think Difference of Perfect Squares: (a + b)(a – b) = (a2 – b2)

Example:

[pic] and [pic] are conjugates.

1. [pic] 2. [pic] 3. [pic]

HW: p. 590 (33-37) p. 595 (14-36 even)

Day 7

Simplify.

1. (5[pic])2 2. (5 + [pic])2

Sec 11-3: Solving Radical Equations

Steps:

1. Get radical with variable alone

2. Square each side to get rid of [pic]

3. Solve

a. If only an x solve.

b. If x2 use factoring or quadratic formula.

4. Check all solutions (extraneous solutions)

Examples.

1. [pic] 2. [pic]

3. [pic] 4. [pic]

5. [pic] 6. [pic][pic]

HW: p. 601 (17-30) & p. 844 Lesson 11-2 (7, 14, 23)

Day 8

More Radical Equations

Steps:

1. Get radical with variable alone

2. Square each side to get rid of [pic]

3. Solve

a. If only an x solve.

b. If x2 use factoring or quadratic formula.

4. Check all solutions (extraneous solutions)

Solve and check.

1. [pic] 2. [pic]

3. [pic] 4. [pic]

Application Problem

Tsunamis, or large tidal waves, are generated by undersea earthquakes in the Pacific Ocean. The speed of the tsunami in meters per second is

s = 3.1[pic], where d is the depth of the ocean in meter.

5. Find the speed of the tsunami if the depth of the water is 10 meters.

6. Find the depth of the water if a tsunami’s speed is 240 meters per second.

HW: p. 601 (31-40) & p. 844 Lesson 11-2 (17, 18, 25)

Day 9

Practice for Quiz 11-2

Add or Subtract *Combine Like Terms

1. [pic] +[pic]

Multiply

2. [pic](5 + 2[pic]) 3. (5 + [pic])(7 + 3[pic])

Solve *Get [pic] by itself

4. 5 + 2[pic] = 9

Sec 11-4: Pythagorean Theorem

a c (hypotenuse) a2 + b2 = c2

(leg)

hypotenuse

b (leg)

1. 2. a = 9, c = 15, b = ?

11. c

4

3. a = [pic] 4. a = [pic], b = 2[pic], c = ?

b =[pic]

c =?

5. The measures of the sides of a triangle are 8, 11, [pic]. Is it a right triangle?

HW: Pythagorean Theorem WS & Quiz Review WS

***Quiz Tomorrow!

Day 10

Sec 11-5: Distance Formula

d = [pic]

Find the distance between each pair of points, round answers to the nearest tenth.

1. (1, 5), (3, 1) 2. (3, –4), (–4, –4)

Find the missing coordinate, round answers to the nearest tenth.

3. (2, -1) (a, 3) d = 5 4. (5, a) (7, -3) d = [pic]

5. An isosceles triangle has two sides of equal lengths. Determine whether triangle ABC with vertices A(–3, 4), B(5, 2), and C(–1, –5) is an isosceles triangle.

HW: p. 613 (13-19 odd, 33), p. 603 (70-72, bottom 6, 8)

p. 615 (48, 50, 51), & p. 621 (43, 46)

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