125 LearnersLast updated on May 26th, 2025
Square Root of 1241
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 1241.
What is the Square Root of 1241?
The square root is the inverse of the square of the number. 1241 is not a perfect square. The square root of 1241 is expressed in both radical and exponential form. In the radical form, it is expressed as √1241, whereas (1241)^(1/2) in the exponential form. √1241 ≈ 35.2207, 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 1241
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 1241 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1241 is broken down into its prime factors.
Step 1: Finding the prime factors of 1241 Breaking it down, we get 7 x 13 x 13: 7^1 x 13^2
Step 2: Now we found out the prime factors of 1241. The second step is to make pairs of those prime factors. Since 1241 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.
Therefore, calculating 1241 using prime factorization is impossible.
Square Root of 1241 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 1241, we need to group it as 41 and 12.
Step 2: Now we need to find n whose square is less than or equal to 12. We can say n as ‘3’ because 3 x 3 = 9 is lesser than or equal to 12. Now the quotient is 3. After subtracting 9 from 12, the remainder is 3.
Step 3: Now let us bring down 41, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and the quotient. Now we get 6n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 341. Let us consider n as 5. Now 65 x 5 = 325.
Step 6: Subtract 325 from 341; the difference is 16, and the quotient is 35.
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 1600.
Step 8: Now we need to find the new divisor, which is 5, because 705 x 5 = 3525.
Step 9: Subtracting 3525 from 1600 gives the result -1925, so adjust n to 2, making the divisor 702 x 2 = 1404.
Step 10: Subtracting 1404 from 1600 gives the result 196.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values, continue till the remainder is zero.
So the square root of √1241 is approximately 35.22.
Square Root of 1241 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 1241 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1241. The smallest perfect square less than 1241 is 1225 (35^2), and the largest perfect square more than 1241 is 1296 (36^2). √1241 falls somewhere between 35 and 36.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (1241 - 1225) ÷ (1296 - 1225) = 16 ÷ 71 = 0.22535 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 35 + 0.225 ≈ 35.225, so the square root of 1241 is approximately 35.225.
Common Mistakes and How to Avoid Them in the Square Root of 1241
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 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 ≈ 7.071, and there is also -7.071, 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: √(12+24) ≠ √12 + √24, which is the wrong method of using roots. The right way of using roots 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, the correct answer is √50 ≈ 7.071.
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 1241 Examples
Problem 1
Can you help Max find the hypotenuse of a right triangle if its other two sides are 1241 and 1?
The hypotenuse is approximately 35.237.
Explanation
Using the Pythagorean theorem:
Hypotenuse^2 = 1241^2 + 1^2.
Taking the square root:
Hypotenuse ≈ √(1241^2 + 1) ≈ √1242 ≈ 35.237.
Therefore, the hypotenuse is approximately 35.237.
Problem 2
A square-shaped garden measuring 1241 square feet is built; if each of the sides is √1241, what will be the square feet of half of the garden?
620.5 square feet
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 1241 by 2, we get 620.5.
So half of the garden measures 620.5 square feet.
Problem 3
Calculate √1241 x 5.
176.1035
Explanation
The first step is to find the square root of 1241 which is approximately 35.2207.
The second step is to multiply 35.2207 by 5.
So 35.2207 x 5 ≈ 176.1035.
Problem 4
What will be the square root of (1236 + 5)?
The square root is approximately 35.221.
Explanation
To find the square root, we need to find the sum of (1236 + 5).
1236 + 5 = 1241, and then √1241 ≈ 35.221.
Therefore, the square root of (1236 + 5) is approximately ±35.221.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √1241 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle as approximately 110.4414 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1241 + 20)
≈ 2 × (35.2207 + 20)
≈ 2 × 55.2207
≈ 110.4414 units.
FAQ on Square Root of 1241
1.What is √1241 in its simplest form?
2.Mention the factors of 1241.
3.Calculate the square of 1241.
4.Is 1241 a prime number?
5.1241 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 1241?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 1241?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 1241
- 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; however, it is always the positive square root that is more prominent due to its uses in the real world. That is the reason it is also known as the principal square root.
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.
- Long division method: The long division method is a way of finding the square root of a number by dividing and iterating through steps to reach an accurate decimal approximation.
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About BrightChamps in Bahrain
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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