Evaluate the square root of 9604 using prime factorization
9604
1372×7
196×7×7
28×7×7×7
4×7×7×7×7
2×2×7×7×7×7
2^2×7^4
divide by 2:
2,4802
2,2,2401
2,2,7,343
2,2, 7,7,49
2,2,2,7,7,7,7
taking the even pairs of roots out:
2,7,7,
sqrt=98
To evaluate the square root of 9604 using prime factorization, we need to identify the prime factors of 9604.
Step 1: Find the prime factors
First, we can divide 9604 by the smallest prime number, which is 2. Dividing by 2, we get 4802. Continuing to divide by 2 gives us 2401. Dividing by 7 will further simplify this expression.
2 × 2 × 2 × 7 × 7 × 7 = 9604
So, 9604 = 2^3 × 7^3
Step 2: Determine the square root
To evaluate the square root of 9604 using prime factorization, we can take the square root of both the base and the exponents.
√(9604) = √(2^3 × 7^3)
√(9604) = √(2^3) × √(7^3)
Simplifying the radicals:
√(9604) = 2^(3/2) × 7^(3/2)
√(9604) = 2 × 7^(3/2)
Hence, the square root of 9604 using prime factorization is 2 × 7^(3/2).