Name_______________________________

Radical Worksheet #1: Prime Factorization

For each number, make a factor tree, then write the prime factorization on the line with the factors in order.

1.) 27 2.) 48 3.) 108

______________ ________________ ________________

4.) 96 5.) 36 6.) 225

______________ ________________ ________________

7.) 340 8.) 336 9.) 72

______________ ________________ ________________

10.) 81 11.) 252 12.) 144

______________ ________________ ________________

13.) 78 14.) 92 15.) 212

______________ ________________ ________________

16.) 624 17.) 720 18.) 63

______________ ________________ ________________

Name_________________________

Radical Worksheet #2:Simplifying Radicals

Write each radical in simplest form (no decimals).

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

Name_________________________

Radical Worksheet #3:Simplifying Radicals

Write each radical in simplest form (no decimals).

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

Name_________________________

Radical Worksheet #4:Simplifying Square Roots

Write each radical in simplest form (no decimals).

1. 2. 3.

4. 5. 6.

7. 8. 9.

Name Radical Worksheet #5:Simplifying all Radicals

Write each radical in simplest form. No decimals!!!

1.) 2.) 3.)

4.) 5.) 6.)

7.) 8.) 9.)

10.) √63 11.) 5√48 12.)

13.) 14.) 15.)

Name_______________________________

Radical Worksheet #6: Adding & Subtracting Square Roots

Simplify the radical expressions.

1.) 2.)

3.) 4.)

5.) 6.)

7.) 8.)

9.) 10.)

Name_______________________________

Radical Worksheet #7: Simplify/Add/Subtract Roots

Simplify each expression.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10.) 11.)

12.) 13.)

Name ______

Radical Worksheet #8: Simplify/Add/Subtract

Simplify each expression.

1.) √125 2.) 5√252 3.)

4.) 5.) 6.)

7.) 8.) 9.)

10.) 11.)

12.) 13.)

14.) 15.)

Name_______________________________

Radical Worksheet #9:Solving Radical Equations

Solve each radical equation. Check your solutions.

1.) 2.)

3.) 4.)

5.) 6.)

7.) 8.)

Name_______________________________

Radical Worksheet #10:Solving Radical Equations

Solve each radical equation. Check your solutions and show your check.

1.) 2.)

3.) 4.) √ x+3=11

5.) 6.) 8+√7 x+2=12

7.) 8.) √2 x+1−5=16

9.) 10.) −1+√5 x−1=7

Name_______________________________

Radical Worksheet #11: Square Roots Review

Simplify each radical expression. You cannot have decimals in your answers.

1. 2. 3.

4. 5. 6.

7. 8. 9.

Solve each radical equation. Check your solutions.

10. 11. 12. 2+√5 x−1=9

Name_______________________________

Algebra Worksheet #12: Distance & Midpoint

Distance Formula

Midpoint Formula M=( x1+x2

2,

y1+ y2

2 )For each of the following sets of ordered pairs, find the distance between the points and the midpoint using the formulas above.

1) (0, 4), (8, -3) 2) (-2, 8), (6, 0)

3) (-3, -1), (7, 4) 4) (9, -2), (3, 6)

5) (-5.2, -8.6), (1.3, 6.5) 6) (7.1, 4.9), (-2.3, -5.5)

Name_______________________________

Radical Worksheet #13: Pythagorean Theorem

Find the missing length of the right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse. Be sure to write answers in simplest radical form.

1.) a = 3, b = 4 2.) a = 5, c = 10 3.) b = 3, c = 7

4.) a = 10, b = 24 5.) b = 9, c = 16 6.) a = 14, c = 21

Find the missing length for each triangle.

7.) 8.)

9.) 10.)

30

27

x

6

x

x

8x

158

Name_______________________________

Radical Worksheet #14: Pythagorean Theorem

Find the missing length of the right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse. Be sure to write answers in simplest radical form.

1.) a = 6, b = 8 2.) a = 4, c = 9 3.) b = 2, c = 8

Find the missing length for each triangle.

4.) 5.)

Use the Pythagorean theorem to decide if the following values could be lengths of a right triangle. Show work to support your answer.

6.) 10, 11, 2 7.) 15, 20, 25

8.) 13, 5, 12 9.) 60, 11, 61

10.) 24, 26, 7 11.) 10.1, 9.9, 2

18

11

x

7

x

Name_______________________________

Radical Worksheet #15: Pythagorean/Distance/Midpoint

Use the Pythagorean theorem to find the missing side of each triangle. Leave answers in simplest radical form.

1.) 2.)

3) 4.)

Use the Pythagorean theorem to decide if the following values could be lengths of a right triangle. Show work to support your answer.

5.) 17, 8, 15 6.) 29, 20, 21

7.) 14, 5, 12 8.) 40, 9, 41

For each of the following sets of ordered pairs, find the distance between the points and the midpoint using the formulas above.

9.) (-6, 11), (-4, 8) 10.) (9, -1), (-3, 7)

249

x

5x

17x

15

x

11

Name_______________________________

Radical Worksheet #16: Square Roots Review

Simplify each radical expression. You cannot have decimals in your answers.

1. √28 2. 3√32 3. 3√12⋅4 √20

4.

√54√2 5.

√7√2 6. √20

81

7. 12√5−4 √5 8. 2√2−8√8+3√32 9. 5√27+2√48

Solve each radical equation. Check your solutions.

10. √ x−3=5 11. √ x−5=7 12.√2x+3=√5 x−12

Name_______________________________

Radical Worksheet #17aSquare Roots Review

Simplify each radical expression. You cannot have decimals in your answers.

1. 2. 3.

4. 5. 6.

7. 8. 9.

Solve each radical equation. Check your solutions.

10. 11. 12.

Radical Worksheet #17bSquare Roots Review

Find the length of the missing side of each triangle. Leave your answer in simplest radical form (no decimals).

c2 = a2 + b2

13. 14.

Determine if the given lengths are sides of a right triangle.

15. 5, 3, 4 16. 7, 9, 5

Find the distance between the two points. Round your answer to the nearest tenth.

17. (7, -1), (-10, 2) 18. (-9, 2), (-5, 3)

Find the midpoint of the two points given.

19. (8, -4), (-1, 6) 20. (11, 5), (-2, 9)

14x

8

x