122 LearnersLast updated on May 26th, 2025
Square Root of 1282
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1282.
What is the Square Root of 1282?
The square root is the inverse of the square of a number. 1282 is not a perfect square. The square root of 1282 is expressed in both radical and exponential forms. In radical form, it is expressed as √1282, whereas in exponential form it is (1282)^(1/2). √1282 ≈ 35.7931, 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 1282
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 1282 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1282 is broken down into its prime factors.
Step 1: Finding the prime factors of 1282 Breaking it down, we get 2 × 641.
Step 2: Now we found out the prime factors of 1282. The second step is to make pairs of those prime factors. Since 1282 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 1282 using prime factorization is not feasible for finding its square root.
Square Root of 1282 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 numbers 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 1282, we need to group it as 28 and 12.
Step 2: Now we need to find n whose square is 12. We can say n is ‘3’ because 3 × 3 is less 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 28, making the new dividend 328. 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 × n ≤ 328. Let us consider n as 5, now 65 × 5 = 325.
Step 6: Subtracting 325 from 328, the difference is 3, 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 300.
Step 8: Now we need to find the new divisor, which is 705, because 705 × 5 = 3525.
Step 9: Subtracting 3525 from 3000, we get the result -525.
Step 10: Now the quotient is 35.7.
Step 11: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.
So the square root of √1282 is approximately 35.79.
Square Root of 1282 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 1282 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1282. The smallest perfect square less than 1282 is 1225, and the largest perfect square greater than 1282 is 1369. √1282 falls somewhere between 35 and 37.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1282 - 1225) / (1369 - 1225) = 57 / 144 = 0.3958. 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 + 0.3958 = 35.3958, so the square root of 1282 is approximately 35.39.
Common Mistakes and How to Avoid Them in the Square Root of 1282
Students do make mistakes while finding the square root, like forgetting about the negative square root and 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, 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 and then move on to the second 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 ≈ 7.071067.
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, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1282 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1282?
The area of the square is approximately 1646.39 square units.
Explanation
The area of the square = side².
The side length is given as √1282.
Area of the square = side² = √1282 × √1282 ≈ 35.79 × 35.79 ≈ 1646.39.
Therefore, the area of the square box is approximately 1646.39 square units.
Problem 2
A square-shaped building measuring 1282 square feet is built; if each of the sides is √1282, what will be the square feet of half of the building?
641 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1282 by 2, we get 641.
So half of the building measures 641 square feet.
Problem 3
Calculate √1282 × 5.
178.965
Explanation
The first step is to find the square root of 1282, which is approximately 35.79.
The second step is to multiply 35.79 by 5.
So 35.79 × 5 = 178.965.
Problem 4
What will be the square root of (1282 + 8)?
The square root is approximately 36.06.
Explanation
To find the square root, we need to find the sum of (1282 + 8).
1282 + 8 = 1290, and then √1290 ≈ 36.06.
Therefore, the square root of (1282 + 8) is approximately ±36.06.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1282 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 147.58 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1282 + 38)
≈ 2 × (35.79 + 38)
= 2 × 73.79
≈ 147.58 units.
FAQ on Square Root of 1282
1.What is √1282 in its simplest form?
2.Mention the factors of 1282.
3.Calculate the square of 1282.
4.Is 1282 a prime number?
5.1282 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 1282?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 1282?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 1282
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, which is √16 = 4.
- Irrational number: An irrational number 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 usually the positive square root that is more widely used in practical applications.
- Prime factorization: The process of expressing a number as the product of its prime factors.
- Long division method: A step-by-step process used to find the square root of non-perfect squares by dividing the number into smaller, more manageable parts.
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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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