117 LearnersLast updated on May 26th, 2025
Square Root of 3725
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. Square roots are used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 3725.
What is the Square Root of 3725?
The square root is the inverse of the square of the number. 3725 is not a perfect square. The square root of 3725 is expressed in both radical and exponential form. In the radical form, it is expressed as √3725, whereas (3725)^(1/2) in the exponential form. √3725 ≈ 61.049, 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 3725
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 3725 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3725 is broken down into its prime factors.
Step 1: Finding the prime factors of 3725 Breaking it down, we get 5 x 5 x 149 = 5^2 x 149
Step 2: Now we have found the prime factors of 3725. The second step is to make pairs of those prime factors. Since 3725 is not a perfect square, the digits of the number can’t be grouped in pairs completely.
Therefore, calculating 3725 using prime factorization alone does not yield an exact square root.
Square Root of 3725 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 3725, we can group it as 37 and 25.
Step 2: Now we need to find n whose square is less than or equal to 37. We can say n is 6 because 6 x 6 = 36, which is less than 37. Now the quotient is 6, and after subtracting 36 from 37, the remainder is 1.
Step 3: Bring down the next pair of numbers, which is 25, making the new dividend 125.
Step 4: Add the old divisor with the same number 6 + 6 = 12, which will be part of our new divisor.
Step 5: The next step is finding 12n × n ≤ 125. Let us consider n as 1, now 121 x 1 = 121, which is less than 125.
Step 6: Subtract 121 from 125; the difference is 4. The quotient is 61.
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 zeros to the dividend. Now the new dividend is 400.
Step 8: Now we need to find the new divisor that is 122 because 1223 x 3 = 366
Step 9: Subtracting 366 from 400, we get the result 34.
Step 10: Now the quotient is 61.0.
Step 11: Continue doing these steps until we get two numbers after the decimal point.
So the square root of √3725 is approximately 61.05.
Square Root of 3725 by Approximation Method
The approximation method is another method for finding the 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 3725 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √3725. The smallest perfect square less than 3725 is 3600, and the largest perfect square more than 3725 is 3844. √3725 falls somewhere between 60 and 62.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (3725 - 3600) / (3844 - 3600) = 0.625. 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 60 + 0.625 = 60.625, so the square root of 3725 is approximately 60.625.
Common Mistakes and How to Avoid Them in the Square Root of 3725
Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Let us look at a few common 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, √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 that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before moving on to the second step.
For example, √(12+24) = √12 + √24 is incorrect. The right way is √(12+24) = √36.
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 incorrect; 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 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, resulting in a wrong answer at the end. This may happen in subtracting or elsewhere.
Square Root of 3725 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3725?
The area of the square is approximately 3725 square units.
Explanation
The area of a square = side^2.
The side length is given as √3725.
Area of the square = side^2 = √3725 x √3725 = 3725.
Therefore, the area of the square box is approximately 3725 square units.
Problem 2
A square-shaped garden measuring 3725 square meters is built. If each of the sides is √3725, what will be the square meters of half of the garden?
1862.5 square meters
Explanation
We can divide the given area by 2 as the garden is square-shaped.
Dividing 3725 by 2, we get 1862.5.
So half of the garden measures 1862.5 square meters.
Problem 3
Calculate √3725 x 5.
Approximately 305.25
Explanation
The first step is to find the square root of 3725, which is approximately 61.05.
The second step is to multiply 61.05 by 5.
So 61.05 x 5 ≈ 305.25.
Problem 4
What will be the square root of (3725 + 25)?
The square root is 62.
Explanation
To find the square root, we need to find the sum of (3725 + 25).
3725 + 25 = 3750, and then √3750 ≈ 62.
Therefore, the square root of (3725 + 25) is approximately ±62.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3725 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 198.1 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3725 + 38)
= 2 × (61.05 + 38)
= 2 × 99.05
≈ 198.1 units.
FAQ on Square Root of 3725
1.What is √3725 in its simplest form?
2.Mention the factors of 3725.
3.Calculate the square of 3725.
4.Is 3725 a prime number?
5.3725 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 3725?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 3725?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 3725
- Square root: A square root is the inverse of a square. For 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, but the principal square root is the positive square root, which is used more often in practical applications.
- Long division method: A technique to find square roots of large numbers that are not perfect squares by dividing and estimating.
- Approximation method: A method to estimate the square root of a number by finding closer perfect squares and using interpolation.
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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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