Math Problem Statement
solve square of 676 using prime factor
Solution
To solve the square root of using prime factorization, we follow these steps:
-
Prime Factorization of 676:
We begin by finding the prime factors of 676.- 676 is an even number, so we divide it by 2:
- Now, 338 is still even, so we divide it by 2 again:
- Next, 169 is not divisible by 2, so we try dividing it by 13:
- So, 169 is .
-
Prime Factors:
Therefore, the prime factorization of 676 is: -
Taking the Square Root:
To find the square root of 676, we take the square root of each factor:
Thus, the square root of 676 is .
Would you like further details or have any questions?
Here are five related questions for practice:
- What is the prime factorization of 169?
- How do you find the square root of 144 using prime factorization?
- What is the prime factorization of 196, and what is its square root?
- Can you determine the square root of 1024 using prime factorization?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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