Math Problem Statement
find the square root of 17576 by prime factorization method
Solution
To find the square root of 17,576 using the prime factorization method, we follow these steps:
Step 1: Prime Factorization of 17,576
First, divide 17,576 by the smallest prime number (2 in this case) until it can't be divided by 2 anymore.
Since 2,197 is odd, we try dividing by the next smallest prime number, 3. It's not divisible by 3, so we try 7, 11, 13, 17, 19, and eventually:
Now, 169 can be factored further:
So, the prime factorization of 17,576 is:
Step 2: Taking the Square Root
To find the square root, we pair the prime factors:
For square root, we take one factor from each pair. From , we can take one factor of 2 (since one pair is available), and from , we take 13.
Thus, the square root of 17,576 is 26.
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Related Questions:
- How would you find the square root of 225 using the prime factorization method?
- What is the prime factorization of 64, and how would you find its square root?
- How does the prime factorization method compare to the long division method for square roots?
- Can all numbers be factored into primes to find their square roots?
- What is the cube root of 8,000 using the prime factorization method?
Tip:
Prime factorization is useful for finding exact roots, but for large numbers, approximation methods (like estimation) are often more practical.
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Math Problem Analysis
Mathematical Concepts
Prime Factorization
Square Roots
Number Theory
Formulas
Square root formula using prime factorization
Theorems
Prime Factorization Theorem
Suitable Grade Level
Grades 6-8