Find the square root of a number 529 by prime factorization method.

To find the square root of 529 using the prime factorization method, we first need to factor the number into its prime components.

Step 1: Prime Factorization

We start by dividing 529 by the smallest prime number, which is 2. Since 529 is odd, we move to the next prime number, 3. We continue this process:

• 529 ÷ 3 = not divisible
• 529 ÷ 5 = not divisible
• 529 ÷ 7 = not divisible
• 529 ÷ 11 = not divisible
• 529 ÷ 13 = 40.69 (not divisible)
• 529 ÷ 17 = not divisible
• 529 ÷ 19 = not divisible
• 529 ÷ 23 = not divisible
• 529 ÷ 29 = not divisible
• 529 ÷ 37 = 14.32 (not divisible)
• 529 ÷ 23 = 23 (exactly)

We find that:

• 529 = 23 × 23

Step 2: Finding the Square Root

Since 529 can be expressed as the product of the prime number 23 multiplied by itself, we can conclude that:

Square Root of 529 = 23

Final Result

The square root of 529 is 23.