101 LearnersLast updated on May 26th, 2025
Square Root of 1256
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 1256.
What is the Square Root of 1256?
The square root is the inverse of the square of a number. 1256 is not a perfect square. The square root of 1256 is expressed in both radical and exponential form. In radical form, it is expressed as √1256, whereas (1256)^(1/2) in exponential form. √1256 ≈ 35.433, 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 1256
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 1256 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1256 is broken down into its prime factors.
Step 1: Finding the prime factors of 1256 Breaking it down, we get 2 x 2 x 2 x 157: 2^3 x 157^1
Step 2: Now we have found the prime factors of 1256. The second step is to make pairs of those prime factors. Since 1256 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √1256 using prime factorization is not feasible.
Square Root of 1256 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 1256, we group it as 56 and 12.
Step 2: Now we need to find n whose square is ≤ 12. We can say n is ‘3’ because 3 x 3 is 9, which is less than 12. Now the quotient is 3, and after subtracting, 12 - 9, the remainder is 3.
Step 3: Now let us bring down 56 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 is now 6n. We need to find the value of n such that 6n x n ≤ 356. Let us consider n as 5, now 6 x 5 x 5 = 150.
Step 5: Subtract 150 from 356, the difference is 206, and the quotient becomes 35.
Step 6: 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 20600.
Step 7: Now we need to find a new digit for the divisor, which is 354, because 3544 x 4 = 14176.
Step 8: Subtract 14176 from 20600, we get 6424. Step 9: Continue doing these steps until we get two numbers after the decimal point.
The square root of √1256 is approximately 35.43.
Square Root of 1256 by Approximation Method
The approximation method is another way to find 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 1256 using the approximation method.
Step 1: We need to find the closest perfect squares around √1256. The smallest perfect square less than 1256 is 1225, and the largest perfect square greater than 1256 is 1296. √1256 falls somewhere between 35 and 36.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (1256 - 1225) / (1296 - 1225) = 31 / 71 ≈ 0.436 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 + 0.436 ≈ 35.436, so the square root of 1256 is approximately 35.436.
Common Mistakes and How to Avoid Them in the Square Root of 1256
Students make mistakes while finding the square root, such as 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 = 7.07, there is also -7.07 which should not be forgotten.
Square Root of 1256 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1256?
The area of the square is 1576.826 square units.
Explanation
The area of a square = side².
The side length is given as √1256.
Area of the square = side² = √1256 x √1256 ≈ 35.433 x 35.433 ≈ 1576.826.
Therefore, the area of the square box is approximately 1576.826 square units.
Problem 2
A square-shaped garden measuring 1256 square feet is designed. If each of the sides is √1256, what will be the square feet of half of the garden?
628 square feet
Explanation
We can divide the given area by 2 as the garden is square-shaped.
Dividing 1256 by 2 = 628.
So half of the garden measures 628 square feet.
Problem 3
Calculate √1256 x 2.
70.866
Explanation
The first step is to find the square root of 1256, which is approximately 35.433.
The second step is to multiply 35.433 by 2.
So, 35.433 x 2 ≈ 70.866.
Problem 4
What will be the square root of (1256 + 16)?
The square root is approximately 36.
Explanation
To find the square root, we need to find the sum of (1256 + 16).
1256 + 16 = 1272, and then √1272 ≈ 35.682.
Therefore, the square root of (1256 + 16) is approximately 35.682.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1256 units and the width ‘w’ is 30 units.
We find the perimeter of the rectangle as approximately 140.866 units.
Explanation
The perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1256 + 30)
= 2 × (35.433 + 30)
= 2 × 65.433
≈ 130.866 units.
FAQ on Square Root of 1256
1.What is √1256 in its simplest form?
2.Mention the factors of 1256.
3.Calculate the square of 1256.
4.Is 1256 a prime number?
5.1256 is divisible by?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 1256?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 1256?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 1256
- Square root: A square root is the inverse of a square. Example: 4² = 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 has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Decimal: If a number has a whole number and a fractional part, it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 18 is 2 x 3 x 3.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
