SQUARE ROOT BY PRIME FACTORIZATION WORKSHEET

Find the square root of each of the following numbers by prime factorization.

1)  36  

2) 324

3)  625

4)  4096

5)  400

6)  144

7)  1024

8)  256

9)  2025

10)  3136

Answers

1. Answer :

√36 =  √(2 ⋅ 2 ⋅ 3 ⋅ 3)

= 2 ⋅ 3

= 6

2. Answer :

√324 = √(2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)

= 2 ⋅ 3 ⋅ 3

= 18

3. Answer :

√625 = √(5 ⋅ 5 ⋅ 5 ⋅ 5)

= 5 ⋅ 5

= 25

4. Answer :

√4096 = √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2)

= 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2

= 64

5. Answer :

√400 = √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5)

= 2 ⋅ 2 ⋅ 5

= 20

6. Answer :

√144 = √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3)

= 2 ⋅ 2 ⋅ 3

= 12

7. Answer :

√1024 = √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2)

= 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2

= 32

8. Answer :

√256 = √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2)

= 2 ⋅ 2 ⋅ 2 ⋅ 2

= 16

9. Answer :

√2025 = √(5 ⋅ 5 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)

= 5 ⋅ 3 ⋅ 3

= 45

10. Answer :

√3136 = √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 7 ⋅ 7)

= 2 ⋅ 2 ⋅ 2 ⋅ 7

= 56

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