What is the simplest form of $\sqrt{3,025}$?
16
55
$5^2\left(11^2\right)$
$5^2+\left(11^2\right)$
Answer (1)
Find the prime factorization of 3,025: 3025 = 5 2 × 1 1 2 .
Take the square root: 3 , 025 = 5 2 × 1 1 2 .
Simplify the square root: 5 2 × 1 1 2 = 5 × 11 .
Calculate the final answer: 5 × 11 = 55 .
Explanation
Problem Analysis We are asked to find the simplest form of 3 , 025 . The factor tree (which is not provided but we can assume it exists and leads to the prime factorization) will help us find the prime factors of 3,025.
Prime Factorization From the problem, we can deduce that 3025 = 5 × 5 × 11 × 11 = 5 2 × 1 1 2 .
Taking the Square Root Now, we take the square root of 3,025: 3 , 025 = 5 2 × 1 1 2 .
Simplifying the Square Root Using the property of square roots, we can simplify this as 5 2 × 1 1 2 = 5 2 × 1 1 2 = 5 × 11 .
Final Calculation Finally, we multiply 5 and 11 to get 5 × 11 = 55 . Therefore, the simplest form of 3 , 025 is 55.
Examples
Understanding square roots is essential in various real-life situations. For example, when calculating the dimensions of a square area, such as a garden or a room, if you know the area, you can find the length of one side by taking the square root of the area. If a square garden has an area of 3,025 square feet, then the length of each side is 3 , 025 = 55 feet. This concept is also used in construction, engineering, and design to ensure accurate measurements and proportions.
