128 LearnersLast updated on May 26th, 2025
Square Root of 1284
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 1284.
What is the Square Root of 1284?
The square root is the inverse of the square of the number. 1284 is not a perfect square. The square root of 1284 is expressed in both radical and exponential form. In the radical form, it is expressed as √1284, whereas (1284)^(1/2) in the exponential form. √1284 ≈ 35.8297, 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 1284
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 and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1284 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1284 is broken down into its prime factors:
Step 1: Finding the prime factors of 1284 Breaking it down, we get 2 x 2 x 3 x 107: 2^2 x 3^1 x 107^1
Step 2: Now we found out the prime factors of 1284. The second step is to make pairs of those prime factors. Since 1284 is not a perfect square, the digits of the number can’t be grouped in pairs that make perfect squares.
Therefore, calculating 1284 using prime factorization does not yield an exact square root.
Square Root of 1284 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 1284, we need to group it as 12 and 84.
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 less than 12. Now the quotient is 3 after subtracting 12 - 9, the remainder is 3.
Step 3: Now let us bring down 84, 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 6n. We need to find the value of n for which 6n x n ≤ 384. Let us consider n as 6, now 66 x 6 = 396. However, this is more than 384, so we try n as 5.
Step 5: The next step is finding 65 x 5 = 325, which is less than 384.
Step 6: Subtracting 325 from 384, the difference is 59, and the quotient is 35.
Step 7: Since the remainder is less than the divisor, we add a decimal point and bring down 00. The new dividend is 5900.
Step 8: Continuing this process, we find subsequent digits after the decimal, obtaining an approximate square root of √1284 ≈ 35.83.
Square Root of 1284 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 1284 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √1284. The smallest perfect square less than 1284 is 1225 (35^2), and the largest perfect square greater than 1284 is 1369 (37^2). √1284 falls somewhere between 35 and 37.
Step 2: Now we apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (1284 - 1225) / (1369 - 1225) = 59 / 144 ≈ 0.4097. 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: 35 + 0.4097 = 35.4097, so the approximate square root of 1284 is 35.4097.
Common Mistakes and How to Avoid Them in the Square Root of 1284
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 has both positive and negative square roots. However, we usually take 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 ≈ 7.071067, not simply 7.
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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1284 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1284?
The area of the square is 1284 square units.
Explanation
The area of the square = side^2.
The side length is given as √1284.
Area of the square = side^2 = √1284 x √1284 = 1284
Therefore, the area of the square box is 1284 square units.
Problem 2
A square-shaped building measuring 1284 square feet is built; if each of the sides is √1284, what will be the square feet of half of the building?
642 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1284 by 2 = we get 642
So half of the building measures 642 square feet.
Problem 3
Calculate √1284 x 5.
179.1485
Explanation
The first step is to find the square root of 1284, which is approximately 35.8297.
The second step is to multiply 35.8297 with 5.
So 35.8297 x 5 ≈ 179.1485
Problem 4
What will be the square root of (784 + 500)?
The square root is 36.
Explanation
To find the square root, we need to find the sum of (784 + 500).
784 + 500 = 1284, and then √1284 ≈ 35.83.
Therefore, the square root of (784 + 500) is approximately 35.83.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1284 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as 171.6594 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1284 + 50)
≈ 2 × (35.8297 + 50)
≈ 2 × 85.8297
≈ 171.6594 units.
FAQ on Square Root of 1284
1.What is √1284 in its simplest form?
2.Mention the factors of 1284.
3.Calculate the square of 1284.
4.Is 1284 a prime number?
5.1284 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 1284?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 1284?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 1284
- 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.
- Approximation: The process of finding a value that is close enough to the correct value, often with a specified degree of accuracy, is approximation.
- Long division method: A method for dividing numbers and finding the square root of non-perfect squares. It involves dividing, multiplying, and subtracting in a sequence.
- Prime factorization: The process of expressing a number as a product of its prime 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.
Fun Fact
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