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
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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