100 LearnersLast updated on May 26th, 2025
Square Root of 2625
If a number is multiplied by the same number, the result is a square. The inverse operation is finding the square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 2625.
What is the Square Root of 2625?
The square root is the inverse of squaring a number. 2625 is not a perfect square. The square root of 2625 can be expressed in both radical and exponential form. In radical form, it is expressed as √2625, whereas in exponential form it is (2625)^(1/2). √2625 ≈ 51.23475, which is an irrational number because it cannot be expressed as a simple fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 2625
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 2625, methods such as the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2625 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2625 is broken down into its prime factors:
Step 1: Finding the prime factors of 2625 Breaking it down, we get 5 x 5 x 3 x 3 x 29: 5^2 x 3^2 x 29
Step 2: Now that we have found the prime factors of 2625, the second step is to make pairs of those prime factors. Since 2625 is not a perfect square, it is impossible to pair all the digits of the number completely.
Therefore, calculating √2625 using prime factorization alone is not feasible.
Square Root of 2625 by Long Division Method
The long division method is used for non-perfect square numbers. In this method, we find 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 2625, we need to group it as 25 and 26.
Step 2: Now, we need to find a number whose square is less than or equal to 26. We can say it is '5' because 5^2 = 25, which is less than or equal to 26. The quotient is 5, and after subtracting, 26 - 25, the remainder is 1.
Step 3: Bring down the next pair of digits (25), making the new dividend 125. Add the previous divisor (5) to itself to make the new divisor 10.
Step 4: Now, we need to find a digit that, when added to 10 and multiplied by the same digit, the product is less than or equal to 125. Let's choose 1. So, 101 x 1 = 101.
Step 5: Subtract 101 from 125, the difference is 24, and the quotient is 51.
Step 6: Since the new dividend is smaller than the new divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 2400.
Step 7: Find the new divisor, which is 102. Choose a digit, say 4, such that 1024 x 4 = 4096.
Step 8: Subtract 4096 from 2400, resulting in a negative number, so we need to adjust our choice. Choose 2 instead, so 1022 x 2 = 2044.
Step 9: Now, the remainder is 356, and the quotient becomes 51.2.
Step 10: Continue these steps until we get the desired precision.
The square root of √2625 ≈ 51.23475.
Square Root of 2625 by Approximation Method
The approximation method is another way to find square roots. 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 2625 using the approximation method.
Step 1: Identify the closest perfect squares to √2625. The smallest perfect square less than 2625 is 2500, and the largest perfect square greater than 2625 is 2704. √2625 falls somewhere between 50 and 52.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (2625 - 2500) / (2704 - 2500) ≈ 0.125 Add this value to the square root of the nearest smaller perfect square: 50 + 0.125 = 50.125.
However, further refining through the long division method, we get √2625 ≈ 51.23475.
Common Mistakes and How to Avoid Them in the Square Root of 2625
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let us look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It's important for students to remember that a number has both positive and negative square roots. However, we typically focus on the positive square root as it is the most relevant in practical applications.
For example: √50 = 7.071, but there is also -7.071 which should not be overlooked.
Square Root of 2625 Examples
Problem 1
Can you help Max find the area of a square if its side length is given as √2625?
The area of the square is approximately 2625 square units.
Explanation
The area of the square = side².
The side length is given as √2625.
Area of the square = side²
= √2625 x √2625
= 2625.
Therefore, the area of the square is approximately 2625 square units.
Problem 2
A square-shaped building measuring 2625 square feet is built. If each of the sides is √2625, what will be the square feet of half of the building?
1312.5 square feet
Explanation
Since the building is square-shaped, we can divide the given area by 2.
Dividing 2625 by 2 = we get 1312.5.
So, half of the building measures 1312.5 square feet.
Problem 3
Calculate √2625 x 5.
Approximately 256.17375
Explanation
The first step is to find the square root of 2625, which is approximately 51.23475.
The second step is to multiply 51.23475 by 5.
So, 51.23475 x 5 ≈ 256.17375.
Problem 4
What will be the square root of (2625 + 75)?
Approximately 52
Explanation
To find the square root, we need to find the sum of (2625 + 75).
2625 + 75 = 2700, and then √2700 ≈ 52.
Therefore, the square root of (2625 + 75) is approximately ±52.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2625 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 202.4695 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2625 + 50)
≈ 2 × (51.23475 + 50)
= 2 × 101.23475
≈ 202.4695 units.
FAQ on Square Root of 2625
1.What is √2625 in its simplest form?
2.Mention the factors of 2625.
3.Calculate the square of 2625.
4.Is 2625 a prime number?
5.2625 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 2625?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 2625?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 2625
- Square root: A square root is the inverse operation of squaring a number. Example: 4² = 16, and the inverse of the square is the square root, that is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, the positive square root is more commonly used in practical applications. This is known as the principal square root.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 30 is 2 x 3 x 5.
- Long division method: The long division method is a process used to divide large numbers to find the square root or solve other division problems.
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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.
