120 LearnersLast updated on May 26th, 2025
Square Root of 3925
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 3925.
What is the Square Root of 3925?
The square root is the inverse of the square of the number. 3925 is not a perfect square. The square root of 3925 is expressed in both radical and exponential form. In the radical form, it is expressed as √3925, whereas (3925)^(1/2) in the exponential form. √3925 ≈ 62.641839, 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 3925
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 3925 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3925 is broken down into its prime factors:
Step 1: Finding the prime factors of 3925 Breaking it down, we get 5 x 5 x 157: 5^2 x 157^1
Step 2: Now we found out the prime factors of 3925. The second step is to make pairs of those prime factors. Since 3925 is not a perfect square, the digits of the number can’t be grouped in pairs completely.
Therefore, calculating 3925 using prime factorization alone is insufficient.
Square Root of 3925 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 numbers from right to left. In the case of 3925, we need to group it as 39 and 25.
Step 2: Now we need to find n whose square is less than or equal to 39. We can say n as ‘6’ because 6 x 6 = 36, which is less than or equal to 39. Now the quotient is 6, and after subtracting 36 from 39, the remainder is 3.
Step 3: Now let us bring down 25, which is the new dividend. Add the old divisor with the same number 6 + 6, we get 12, which will be our new divisor.
Step 4: The new divisor will be 12n, where n is to be determined such that 12n x n ≤ 325.
Step 5: Let n = 2, so 122 x 2 = 244, which is less than 325.
Step 6: Subtract 244 from 325, the difference is 81, and the quotient becomes 62.
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 8100.
Step 8: Now we need to find the new divisor, which is 124 because 1244 x 4 = 4976.
Step 9: Subtract 4976 from 8100, we get the result 3124.
Step 10: The quotient is 62.6
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √3925 is approximately 62.64.
Square Root of 3925 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 3925 using the approximation method.
Step 1: Now we have to find the closest perfect square of √3925. The smallest perfect square less than 3925 is 3844 (62^2), and the largest perfect square greater than 3925 is 4096 (64^2). √3925 falls somewhere between 62 and 63.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (3925 - 3844) / (4096 - 3844) = 81 / 252 = 0.32 Using the formula, 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 62 + 0.32 = 62.32.
So the square root of 3925 is approximately 62.32 in this approximation.
Common Mistakes and How to Avoid Them in the Square Root of 3925
Students do make mistakes while finding the square root, likewise forgetting about the negative square root, skipping long division methods, etc. 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 has both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √3925 ≈ 62.64, there is also -62.64, 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 that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(100+25) = √100 + √25 is a wrong method of using roots. The right way of using roots is √(100+25) = √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 is wrong, 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 constantly as this will help them keep away from 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 3925 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3925?
The area of the square is approximately 3925 square units.
Explanation
The area of the square = side^2.
The side length is given as √3925.
Area of the square = √3925 x √3925 = 3925.
Therefore, the area of the square box is approximately 3925 square units.
Problem 2
A square-shaped building measuring 3925 square feet is built; if each of the sides is √3925, what will be the square feet of half of the building?
1962.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3925 by 2 = we get 1962.5
So half of the building measures 1962.5 square feet.
Problem 3
Calculate √3925 x 5.
313.21
Explanation
The first step is to find the square root of 3925, which is approximately 62.64.
The second step is to multiply 62.64 with 5.
So 62.64 x 5 ≈ 313.21.
Problem 4
What will be the square root of (3925 + 75)?
The square root is approximately 64
Explanation
To find the square root, we need to find the sum of (3925 + 75).
3925 + 75 = 4000, and then √4000 ≈ 63.245553.
Therefore, the square root of (3925 + 75) is approximately ±63.25.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3925 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 201.28 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3925 + 38)
= 2 × (62.64 + 38)
≈ 2 × 100.64
≈ 201.28 units.
FAQ on Square Root of 3925
1.What is √3925 in its simplest form?
2.Mention the factors of 3925.
3.Calculate the square of 3925.
4.Is 3925 a prime number?
5.3925 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 3925?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 3925?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 3925
- Square root: A square root is the inverse of a square. Example: 4^2 = 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, it is always a positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Prime factorization: A method of expressing a number as the product of its prime factors.
- Long division method: A procedure used for dividing a number to determine its square root, particularly for non-perfect squares.
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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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