128 LearnersLast updated on May 26th, 2025
Square Root of 3649
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 3649.
What is the Square Root of 3649?
The square root is the inverse of the square of the number. 3649 is not a perfect square. The square root of 3649 is expressed in both radical and exponential form. In the radical form, it is expressed as √3649, whereas (3649)^(1/2) in the exponential form. √3649 ≈ 60.374, 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 3649
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 3649 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3649 is broken down into its prime factors.
Step 1: Finding the prime factors of 3649 3649 is a prime number, so its only prime factors are 1 and itself.
Step 2: Since 3649 is not a perfect square and cannot be expressed with repeated prime factors, calculating √3649 using prime factorization is not feasible.
Square Root of 3649 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 3649, we need to group it as 49 and 36.
Step 2: Now we need to find n whose square is 36. We can say n as ‘6’ because 6 × 6 = 36. Now the quotient is 6 and the remainder is 0.
Step 3: Now let us bring down 49 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 the sum of the dividend and quotient. Now we get 12n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 12n × n ≤ 49. Let us consider n as 4, now 12 × 4 = 48.
Step 6: Subtract 49 from 48, the difference is 1, and the quotient is 60.
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 100.
Step 8: Now we need to find the new divisor, which is 120, because 120 × 0 = 0.
Step 9: Subtracting 0 from 100 we get the result 100.
Step 10: Now the quotient is 60.3.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.
So the square root of √3649 is approximately 60.37.
Square Root of 3649 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 3649 using the approximation method.
Step 1: Now we have to find the closest perfect square of √3649. The smallest perfect square less than 3649 is 3600 (60^2), and the largest perfect square greater than 3649 is 3721 (61^2). √3649 falls somewhere between 60 and 61.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (3649 - 3600) ÷ (3721 - 3600) = 49 ÷ 121 ≈ 0.39. 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 + 0.39 ≈ 60.39.
So the square root of 3649 is approximately 60.39.
Common Mistakes and How to Avoid Them in the Square Root of 3649
Students do make mistakes while finding the square root, like 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 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: √3649 ≈ 60.39, there is also -60.39 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 and then move on to the second step.
For example: √(36 + 49) ≠ √36 + √49 is the wrong method of using roots. The right way of using roots is √(36 + 49) = √85.
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: √3649 ≈ 60 is wrong, the correct answer is √3649 ≈ 60.39.
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: √3649 and ∛3649 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 of the sum. This may either happen in subtracting or elsewhere.
Square root of 3649 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3649?
The area of the square is approximately 3649 square units.
Explanation
The area of the square = side^2.
The side length is given as √3649.
Area of the square = side^2 = √3649 × √3649 = 3649.
Therefore, the area of the square box is approximately 3649 square units.
Problem 2
A square-shaped building measuring 3649 square feet is built; if each of the sides is √3649, what will be the square feet of half of the building?
1824.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3649 by 2 gives us 1824.5.
So half of the building measures 1824.5 square feet.
Problem 3
Calculate √3649 × 5.
Approximately 301.95
Explanation
The first step is to find the square root of 3649, which is approximately 60.39.
The second step is to multiply 60.39 by 5.
So 60.39 × 5 ≈ 301.95.
Problem 4
What will be the square root of (3649 + 51)?
The square root is approximately 61.
Explanation
To find the square root, we need to find the sum of (3649 + 51).
3649 + 51 = 3700, and then √3700 ≈ 60.83.
Therefore, the square root of (3649 + 51) is approximately ±60.83.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3649 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 197.78 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3649 + 38)
= 2 × (60.39 + 38)
= 2 × 98.39
= 196.78 units.
FAQ on Square Root of 3649
1.What is √3649 in its simplest form?
2.Mention the factors of 3649.
3.Calculate the square of 3649.
4.Is 3649 a prime number?
5.3649 is divisible by?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 3649?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 3649?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for the Square Root of 3649
- 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.
- Prime number: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. Example: 2, 3, 5, 7, 11, etc.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Long division method: A method used to find the square root of a number by dividing it into pairs of digits, starting from the right, and finding the largest number whose square is less than or equal to the number being divided.
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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
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