how to use prime factorization using Square Root??? Examples Plzz like 3 examples
To use prime factorization with square roots, you need to follow a series of steps. Let's walk through three examples to understand the process better.
Example 1: Find the prime factors of 24 using square root.
Step 1: Take the square root of the number you want to factorize. √24 = 4.898...
Step 2: Start with the smallest prime number, 2, and check if it is a factor of 24. Divide 24 by 2: 24 ÷ 2 = 12.
Step 3: Take the square root of the quotient. √12 = 3.464...
Step 4: Repeat Step 2 with this new quotient, so divide 12 by 2: 12 ÷ 2 = 6.
Step 5: Take the square root again. √6 = 2.449...
Step 6: Continue with Step 2, dividing 6 by 2: 6 ÷ 2 = 3.
Step 7: The final quotient is a prime number. Take the square root of 3: √3 = 1.732...
Therefore, the prime factors of 24 using square root are 2, 2, 2, and 3 (2 × 2 × 2 × 3).
Example 2: Find the prime factors of 56 using square root.
Step 1: Take the square root of 56. √56 = 7.483...
Step 2: Divide by 2. 56 ÷ 2 = 28.
Step 3: Take the square root of 28. √28 = 5.291...
This cannot be divided further, so we proceed to the next prime number: 3.
Step 4: Divide 28 by 3. 28 ÷ 3 = 9.333...
Step 5: Take the square root of 9.333... (rounded to the nearest whole number). √9 ≈ 3.
Therefore, the prime factors of 56 using square root are 2, 2, 2, and 7 (2 × 2 × 2 × 7).
Example 3: Find the prime factors of 100 using square root.
Step 1: Take the square root of 100. √100 = 10.
Step 2: Divide by 2. 100 ÷ 2 = 50.
Step 3: Take the square root of 50. √50 = 7.071...
Step 4: This cannot be divided further by the same prime number, so proceed to the next prime number: 3.
Step 5: Divide 50 by 5. 50 ÷ 5 = 10.
Step 6: Take the square root of 10. √10 = 3.162...
Again, this cannot be divided further, so we stop here.
Therefore, the prime factors of 100 using square root are 2, 2, 5, and 5 (2 × 2 × 5 × 5).
By repeating these steps, you can find the prime factors of any number using square root.