124 LearnersLast updated on May 26th, 2025
Square Root of 1255
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 1255.
What is the Square Root of 1255?
The square root is the inverse of the square of the number. 1255 is not a perfect square. The square root of 1255 is expressed in both radical and exponential form. In the radical form, it is expressed as √1255, whereas (1255)^(1/2) in the exponential form. √1255 ≈ 35.433 and 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 1255
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 1255 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1255 is broken down into its prime factors:
Step 1: Finding the prime factors of 1255. Breaking it down, we get 5 x 251: 5^1 x 251^1.
Step 2: Now we have found the prime factors of 1255. Since 1255 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating 1255 using prime factorization is not feasible.
Square Root of 1255 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 1255, we need to group it as 55 and 12.
Step 2: Now we need to find n whose square is less than or equal to 12. We can say n is ‘3’ because 3 x 3 = 9 is less than or equal to 12. Now the quotient is 3, and after subtracting 9 from 12, the remainder is 3.
Step 3: Now let us bring down 55, which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and 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 x n ≤ 355. Let us consider n as 5; now, 65 x 5 = 325.
Step 6: Subtract 325 from 355; the difference is 30, 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 3000.
Step 8: Now we need to find the new divisor, which is 709 because 709 x 4 = 2836.
Step 9: Subtracting 2836 from 3000, we get the result 164.
Step 10: Now the quotient is 35.4.
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 √1255 is approximately 35.43.
Square Root of 1255 by Approximation Method
The approximation method is another approach 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 1255 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √1255. The smallest perfect square less than 1255 is 1225, and the largest perfect square more than 1255 is 1296. √1255 falls somewhere between 35 and 36.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Largest perfect square - smallest perfect square). Applying the formula (1255 - 1225) ÷ (1296 - 1225) = 30 ÷ 71 ≈ 0.42. Using this formula, we find the decimal approximation of our square root. The next step is adding the value we got initially to the decimal number, which is 35 + 0.42 = 35.42, so the square root of 1255 is approximately 35.42.
Common Mistakes and How to Avoid Them in the Square Root of 1255
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. 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 = 7.07, there is also -7.07 that 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, teach children that simplifying the numbers inside the square root is important before moving to the next step.
For example: √(12+24) = √12 + √24 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 is wrong, 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 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 of the sum. This may happen in subtracting or elsewhere.
Square root of 1255 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1300?
The area of the square is approximately 1300 square units.
Explanation
The area of the square = side^2.
The side length is given as √1300.
Area of the square = side^2 = √1300 x √1300 = 1300.
Therefore, the area of the square box is approximately 1300 square units.
Problem 2
A square-shaped field measuring 1255 square meters is built; if each of the sides is √1255, what will be the square meters of half of the field?
627.5 square meters
Explanation
We can divide the given area by 2 as the field is square-shaped.
Dividing 1255 by 2 = we get 627.5.
So half of the field measures 627.5 square meters.
Problem 3
Calculate √1255 x 5.
177.165
Explanation
The first step is to find the square root of 1255, which is approximately 35.433.
The second step is to multiply 35.433 by 5.
So 35.433 x 5 ≈ 177.165.
Problem 4
What will be the square root of (1300 + 25)?
The square root is 37.
Explanation
To find the square root, we need to find the sum of (1300 + 25).
1300 + 25 = 1325, and then √1325 ≈ 36.4.
Therefore, the square root of (1300 + 25) is approximately 36.4, but for simplification, we use 37.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1300 units and the width ‘w’ is 40 units.
We find the perimeter of the rectangle as 163.6 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1300 + 40)
≈ 2 × (36.06 + 40)
= 2 × 76.06
= 152.12 units.
FAQ on Square Root of 1255
1.What is √1255 in its simplest form?
2.Mention the factors of 1255.
3.Calculate the square of 1255.
4.Is 1255 a prime number?
5.1255 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 1255?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 1255?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 1255
- 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, which 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. This is why it is also known as the principal square root.
- Long division method: A method used for finding the square root of non-perfect squares by dividing and approximating step by step.
- Prime factorization: Breaking down a number into its basic prime number components, used to simplify numbers and solve problems involving factors.
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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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