128 LearnersLast updated on May 26th, 2025
Square Root of 3025
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 3025.
What is the Square Root of 3025?
The square root is the inverse of the square of the number. 3025 is a perfect square. The square root of 3025 is expressed in both radical and exponential form. In the radical form, it is expressed as √3025, whereas (3025)^(1/2) in the exponential form. √3025 = 55, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 3025
The prime factorization method is particularly useful for perfect square numbers. The long division method and approximation method can also be used for checking. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 3025 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3025 is broken down into its prime factors:
Step 1: Finding the prime factors of 3025 Breaking it down, we get 5 × 5 × 11 × 11: 5² × 11²
Step 2: Now we found out the prime factors of 3025. The next step is to make pairs of those prime factors. Since 3025 is a perfect square, the digits of the number can be grouped in pairs. Therefore, √3025 = 5 × 11 = 55.
Square Root of 3025 by Long Division Method
The long division method is used to find the square root of perfect squares as well. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 3025, we need to group it as 30 and 25.
Step 2: Now we need to find n whose square is close to or less than 30. We know 5 × 5 = 25, which is less than 30. So, the quotient is 5, and after subtracting 25 from 30, the remainder is 5.
Step 3: Now let us bring down 25, which is the new dividend. Add the old divisor (5) with itself, 5 + 5, to get 10, which will be our new divisor.
Step 4: The new divisor will be 10n. We need to find the value of n such that 10n × n is close to or less than 525. Let n be 5, then 10 × 5 × 5 = 525.
Step 5: Subtract 525 from 525, the remainder is 0, and the quotient is 55. Thus, the square root of √3025 is 55.
Square Root of 3025 by Approximation Method
The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 3025 using the approximation method.
Step 1: Now we have to find the closest perfect square of √3025. 3025 is itself a perfect square. So, the square root of 3025 is directly 55.
Common Mistakes and How to Avoid Them in the Square Root of 3025
Students do make mistakes while finding the square root, like forgetting about the negative square root or misapplying methods. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √3025 = 55, there is also -55 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before moving on.
For example: √(25 + 100) ≠ √25 + √100. The right way is √(25 + 100) = √125.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them avoid mistakes.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 3025 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3025?
The area of the square is 3025 square units.
Explanation
The area of the square = side².
The side length is given as √3025.
Area of the square = side² = (√3025)² = 55 × 55 = 3025.
Therefore, the area of the square box is 3025 square units.
Problem 2
A square-shaped garden measures 3025 square feet; if each of the sides is √3025, what will be the square feet of half of the garden?
1512.5 square feet
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 3025 by 2 = 1512.5.
So half of the garden measures 1512.5 square feet.
Problem 3
Calculate √3025 × 3.
165
Explanation
The first step is to find the square root of 3025, which is 55.
The second step is to multiply 55 by 3.
So 55 × 3 = 165.
Problem 4
What will be the square root of (2025 + 1000)?
The square root is 55.
Explanation
To find the square root, we need to find the sum of (2025 + 1000).
2025 + 1000 = 3025, and then √3025 = 55.
Therefore, the square root of (2025 + 1000) is ±55.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3025 units and the width ‘w’ is 25 units.
We find the perimeter of the rectangle as 160 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3025 + 25) = 2 × (55 + 25) = 2 × 80 = 160 units.
FAQ on Square Root of 3025
1.What is √3025 in its simplest form?
2.Mention the factors of 3025.
3.Calculate the square of 3025.
4.Is 3025 a prime number?
5.3025 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 3025?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 3025?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 3025
- Square root: A square root is the inverse operation of squaring a number. For example, 5² = 25 and the inverse operation is √25 = 5.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 3025 is a perfect square because it equals 55².
- Rational number: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where q ≠ 0.
- Negative square root: Every positive number has two square roots, one positive and one negative. For example, the square roots of 25 are 5 and -5.
- Long division method: This method is used to find the square root of a number through a step-by-step division process.
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About BrightChamps in Oman
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
