ROOTS OF INTEGERS WORKSHEET

Evaluate each of the following.

1) √4

2) √16

3) √64

4) √144

5)³√27

6) ³√-8

7) ³√512

8) ³√-8000

9) ⁴√64

10) ⁴√81

11) ⁵√32

12) ⁵√243

13) √8

14) √45

15) ³√54

16) √25 + √36

17) √20 + √45

18) 2√18 - √8

19) ³√8 + ³√27

20) √49 + ³√125 + ⁴√256

1. Answer :

√4 = √(2 x 2)

= 9

2. Answer :

√16 = √(4 x 4)

= 4

3. Answer :

√64 = √(8 x 8)

= 8

4. Answer :

√144 = √(12 x 12)

= 12

5. Answer :

³√27 = ³√(3 x 3 x 3)

= 3

6. Answer :

³√-8 = ³√[(-2)(-2)(-2)]

= -2

7. Answer :

³√512 = ³√(8 x 8 x 8)

= 8

8. Answer :

³√-8000 = ³√[(-20)(-20)(-20)]

= -20

9. Answer :

⁴√16 = ⁴√(2 x 2 x 2 x 2)

= 2

10. Answer :

⁴√81 = ⁴√(3 x 3 x 3 x 3)

= 3

11. Answer :

⁵√32 = ⁵√(2 x 2 x 2 x 2 x 2)

= 2

12. Answer :

⁵√243 = ⁵√(3 x 3 x 3 x 3 x 3)

= 3

13. Answer :

√8 = √(2 x 2 x 2)

= 2√2

14. Answer :

√45 = √(3 x 3 x 5)

= 3√5

15. Answer :

³√54 = ³√(3 x 3 x 3 x 2)

= 3³√2

16. Answer :

√25 + √36 = √(5 x 5) + √(6 x 6)

= 5 + 6

= 11

17. Answer :

√20 + √45 = √(2 x 2 x 5) + √(3 x 3 x 5)

= 2√5 + 3√5

= 5√5

18. Answer :

2√18 - √8 = 2√(3 x 3 x 2) - √(2 x 2 x 2)

= 2(3√2) - 2√2

= 6√2 - 2√2

= 4√2

19. Answer :

³√8 + ³√27 = ³√(2 x 2 x 2) + ³√(3 x 3 x 3)

= 2 + 3

= 5

20. Answer :

√49 + ³√125 + ⁴√256 :

= √(7 x 7) + ³√(5 x 5 x 5) + ⁴√(4 x 4 x 4 x 4)

= 7 + 5 + 4

= 16

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