Square Root by Prime Factorization Example Problems. Solution: Step 1: The given number is resolved into its prime factors. 3. Only numbers bigger than or equal to zero have real square roots. Equcation for number 2025 factorization is: 3 * 3 * 3 * 3 * 5 * 5; It is determined that the prime factors of number 2025 are: 3, 5; Prime Factorization Of 2024; Prime Factorization Of 2026 The prime factors of 2025 are 3 and 5. 3. A number bigger than zero has two square roots: one is positive (bigger than zero) and the other is negative (smaller than zero). For example, 2 is the square root of 4, because 2x2=4. (iii) Combine the like square root terms using mathematical operations. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. A square root of a number is a number that, when it is multiplied by itself (squared), gives the first number again. 2. Thew following steps will be useful to find square root of a number by prime factorization. 7. The prime factorization of 2025 = 3 4 •5 2. Solve your math problems using our free math solver with step-by-step solutions. In other words, a composite number is any integer greater than one that is not a prime number. 2. A composite number is a positive integer that has at least one positive divisor other than one or the number itself. 7 \[1764 = 2\times 2\times 3\times 3\times 7\times 7\] Step 2: Identical factors are paired. Find the square root of 1764 using the prime factorization method. 882. 147. (i) Decompose the number inside the square root into prime factors. 49. 441. 1764. 1. (ii) Inside the square root, for every two same numbers multiplied, one number can be taken out of the square root. Worksheet on square root using prime factorization method is useful for the students to prepare well for the exams. The factors of 225 = 3x3x5x5 = 3^2x5^2 Square root of 225 = [3^2x5^2]^0.5 = 3^(2*0.5)*5^(2*0.5) = 3x5 = 15. 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