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find the square root of the following numbers by using factorization method by steps ??
1.10404 ?
2.11664 ?
Anonymous
more than 1 week ago
find the square root of the following numbers by using factorization method by steps ?? 1.10404 ? 2.11664 ?
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ChatGPT
more than 1 week ago
1. 10404
Step 1: Find the prime factors of 10404
10404 = 2^2 * 3^2 * 17^2
Step 2: Take one factor from each pair of prime factors
√10404 = 2 * 3 * 17 = 102
Therefore, the square root of 10404 is 102.
2. 11664
Step 1: Find the prime factors of 11664
11664 = 2^4 * 3^2 * 11^2
Step 2: Take one factor from each pair of prime factors
√11664 = 2^2 * 3 * 11 = 66
Therefore, the square root of 11664 is 66.
Step 1: Find the prime factors of 10404
10404 = 2^2 * 3^2 * 17^2
Step 2: Take one factor from each pair of prime factors
√10404 = 2 * 3 * 17 = 102
Therefore, the square root of 10404 is 102.
2. 11664
Step 1: Find the prime factors of 11664
11664 = 2^4 * 3^2 * 11^2
Step 2: Take one factor from each pair of prime factors
√11664 = 2^2 * 3 * 11 = 66
Therefore, the square root of 11664 is 66.
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Google Gemini AI
more than 1 week ago
1. Square root of 10404 by factorization method.
Step 1: Find the greatest perfect square that divides 10404.
10404 = 2 × 2 × 2601 = 2 × 2 × 3 × 867
Step 2: Take out the perfect square factors in pairs.
√10404 = √(2 × 2 × 3 × 867) = √(2 × 2) × √3 × √867 = 2√3 × √867
Step 3: Find the square root of the remaining factor (if possible).
√867 is not a perfect square. So, we leave it as it is.
Therefore, √10404 = 2√3 × √867
2. Square root of 11664 by factorization method.
Step 1: Find the greatest perfect square that divides 11664.
11664 = 2 × 2 × 2 × 2 × 3 × 191
Step 2: Take out the perfect square factors in pairs.
√11664 = √(2 × 2 × 2 × 2 × 3 × 191) = √(2 × 2) × √(2 × 2) × √3 × √191 = 2 × 2 × √3 × √191 = 4√3 × √191
Step 3: Find the square root of the remaining factor (if possible).
√191 is not a perfect square. So, we leave it as it is.
Therefore, √11664 = 4√3 × √191
Step 1: Find the greatest perfect square that divides 10404.
10404 = 2 × 2 × 2601 = 2 × 2 × 3 × 867
Step 2: Take out the perfect square factors in pairs.
√10404 = √(2 × 2 × 3 × 867) = √(2 × 2) × √3 × √867 = 2√3 × √867
Step 3: Find the square root of the remaining factor (if possible).
√867 is not a perfect square. So, we leave it as it is.
Therefore, √10404 = 2√3 × √867
2. Square root of 11664 by factorization method.
Step 1: Find the greatest perfect square that divides 11664.
11664 = 2 × 2 × 2 × 2 × 3 × 191
Step 2: Take out the perfect square factors in pairs.
√11664 = √(2 × 2 × 2 × 2 × 3 × 191) = √(2 × 2) × √(2 × 2) × √3 × √191 = 2 × 2 × √3 × √191 = 4√3 × √191
Step 3: Find the square root of the remaining factor (if possible).
√191 is not a perfect square. So, we leave it as it is.
Therefore, √11664 = 4√3 × √191
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