120 LearnersLast updated on May 26th, 2025
Square Root of 2125
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, and more. Here, we will discuss the square root of 2125.
What is the Square Root of 2125?
The square root is the inverse of squaring a number. 2125 is not a perfect square. The square root of 2125 is expressed in both radical and exponential form. In radical form, it is expressed as √2125, whereas in exponential form, it is expressed as (2125)^(1/2). √2125 ≈ 46.092, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 2125
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods such as the long-division method and approximation method are used. Let us now learn about these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2125 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2125 is broken down into its prime factors.
Step 1: Finding the prime factors of 2125
Breaking it down, we get 5 x 5 x 5 x 17: 5^3 x 17^1
Step 2: Now we have found the prime factors of 2125. The second step is to make pairs of those prime factors. Since 2125 is not a perfect square, the digits of the number cannot be grouped into pairs. Therefore, calculating √2125 using prime factorization is not possible.
Square Root of 2125 by Long Division Method
The long division method is particularly used for non-perfect square numbers. 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 number from right to left. In the case of 2125, we need to group it as 21 and 25.
Step 2: Now we need to find n whose square is less than or equal to 21. We can say n as ‘4’ because 4 x 4 = 16 is less than 21. The quotient is 4 and the remainder is 5 after subtracting 16 from 21.
Step 3: Now let us bring down 25 which is the new dividend. Add the old divisor with the same number 4 + 4 = 8, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 8n x n ≤ 525. Let us consider n as 6, now 86 x 6 = 516.
Step 6: Subtract 516 from 525, the difference is 9, and the quotient is 46.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 900.
Step 8: Now we need to find the new divisor that is 921 because 921 x 1 = 921 is too large, so we need to adjust until we find the appropriate value.
Step 9: Continue the steps until we reach a satisfactory decimal precision.
So the square root of √2125 is approximately 46.092.
Square Root of 2125 by Approximation Method
The approximation method is another method for finding 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 2125 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √2125. The smallest perfect square less than 2125 is 2025, and the largest perfect square more than 2125 is 2209. √2125 falls somewhere between 45 and 47.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).
Using the formula (2125 - 2025) / (2209 - 2025) ≈ 0.5 We identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 46 + 0.5 = 46.5, but as further refinement shows, it's approximately 46.092.
Common Mistakes and How to Avoid Them in the Square Root of 2125
Students may make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few 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, √50 = 7.07, but there is also -7.07 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving to the next step.
For example, √(12+24) ≠ √12 + √24. The correct method is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
Students should be taught to simplify the numbers inside the square root correctly. This is crucial to avoid mistakes while identifying the approximate value.
For example, √50 ≠ 7; the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root consistently to avoid confusion.
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, and students might skip a step accidentally, resulting in a wrong answer. This may occur in subtracting or elsewhere.
Square Root of 2125 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2125?
The area of the square is approximately 2125 square units.
Explanation
The area of the square = side^2.
The side length is given as √2125.
Area of the square = side^2 = √2125 x √2125 = 2125
Therefore, the area of the square box is approximately 2125 square units.
Problem 2
A square-shaped building measuring 2125 square feet is built; if each of the sides is √2125, what will be the square feet of half of the building?
1062.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2125 by 2 = we get 1062.5
So half of the building measures 1062.5 square feet.
Problem 3
Calculate √2125 x 5.
Approximately 230.46
Explanation
The first step is to find the square root of 2125, which is approximately 46.092.
The second step is to multiply 46.092 by 5.
So 46.092 x 5 ≈ 230.46
Problem 4
What will be the square root of (2025 + 100)?
The square root is approximately 46.092
Explanation
To find the square root, we need to find the sum of (2025 + 100). 2025 + 100 = 2125, and then √2125 ≈ 46.092.
Therefore, the square root of (2025 + 100) is approximately 46.092.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2125 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 192.184 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2125 + 50) = 2 × (46.092 + 50) = 2 × 96.092 ≈ 192.184 units.
FAQ on Square Root of 2125
1.What is √2125 in its simplest form?
2.Mention the factors of 2125.
3.Calculate the square of 2125.
4.Is 2125 a prime number?
5.2125 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 2125?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 2125?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 2125
- Square root: A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse is the square root √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, but the positive square root is often used due to its applications in the real world, known as the principal square root.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 2125 is 5^3 x 17.
- Decimal: A number that consists of a whole number and a fractional part, separated by a decimal point, such as 46.092.
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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.
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