Math Problem Statement

solve square of 676 using prime factor

Solution

To solve the square root of 676676 using prime factorization, we follow these steps:

  1. Prime Factorization of 676:
    We begin by finding the prime factors of 676.

    • 676 is an even number, so we divide it by 2: 676÷2=338676 \div 2 = 338
    • Now, 338 is still even, so we divide it by 2 again: 338÷2=169338 \div 2 = 169
    • Next, 169 is not divisible by 2, so we try dividing it by 13: 169÷13=13169 \div 13 = 13
    • So, 169 is 13213^2.
  2. Prime Factors:
    Therefore, the prime factorization of 676 is: 676=22×132676 = 2^2 \times 13^2

  3. Taking the Square Root:
    To find the square root of 676, we take the square root of each factor: 676=(22)×(132)=2×13=26\sqrt{676} = \sqrt{(2^2) \times (13^2)} = 2 \times 13 = 26

Thus, the square root of 676 is 2626.

Would you like further details or have any questions?

Here are five related questions for practice:

  1. What is the prime factorization of 169?
  2. How do you find the square root of 144 using prime factorization?
  3. What is the prime factorization of 196, and what is its square root?
  4. Can you determine the square root of 1024 using prime factorization?
  5. What is the prime factorization of 900, and what is its square root?

Tip: Always start by checking divisibility by small primes (2, 3, 5) when finding the prime factorization of a number.

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Math Problem Analysis

Mathematical Concepts

Prime Factorization
Square Roots

Formulas

√(a × b) = √a × √b
Prime Factorization

Theorems

Fundamental Theorem of Arithmetic

Suitable Grade Level

Grades 6-8