128 LearnersLast updated on May 26th, 2025
Square Root of 1289
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1289.
What is the Square Root of 1289?
The square root is the inverse of the square of the number. 1289 is not a perfect square. The square root of 1289 is expressed in both radical and exponential form. In radical form, it is expressed as √1289, whereas (1289)^(1/2) in exponential form. √1289 ≈ 35.8997, 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 1289
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 1289, 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 1289 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1289 is broken down into its prime factors.
Step 1: Finding the prime factors of 1289 Breaking it down, we get 1289 = 1 x 1289: 1289 is a prime number.
Step 2: Since 1289 is not a perfect square and is a prime number itself, calculating 1289 using prime factorization is not feasible.
Square Root of 1289 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 1289, we need to group it as 28 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, which is less than 12. Now the quotient is 3, and the remainder is 3 after subtracting 9 from 12.
Step 3: Now let us bring down 89, making the new dividend 389. Add the old divisor (3) with the same number to get 6, which will be our new divisor.
Step 4: The new divisor becomes 6n. We need to find the value of n such that 6n x n ≤ 389. Let us consider n as 6; 66 x 6 = 396, which is greater than 389, so try n = 5; 65 x 5 = 325.
Step 5: Subtract 325 from 389; the difference is 64, and the quotient is 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 6400.
Step 7: Now we need to find the new divisor, which is 719 because 719 x 9 = 6471.
Step 8: Subtract 6471 from 6400, resulting in a negative number, indicating an adjustment needed at the previous step. Backtrack and continue the process with better approximations.
Step 9: Continue doing these steps until two numbers are obtained after the decimal point, or until the desired precision is achieved.
So the square root of √1289 is approximately 35.90.
Square Root of 1289 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 1289 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √1289. The smallest perfect square less than 1289 is 1225 (since 35^2 = 1225), and the largest perfect square greater than 1289 is 1369 (since 37^2 = 1369). √1289 falls between 35 and 37.
Step 2: Use interpolation to approximate the square root. (1289 - 1225)/(1369 - 1225) ≈ 0.4444. Using this result, the approximate square root is 35 + 0.4444 x (37 - 35) = 35.8888, which rounds to approximately 35.90.
Common Mistakes and How to Avoid Them in the Square Root of 1289
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping the long division method, 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 typically consider only the positive square root, as it is the required one in most practical applications.
For example: √50 = 7.07.
There is also -7.07, 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 students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before proceeding to the next step.
For example: √(12+24) ≠ √12 + √24.
The correct method 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 students 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 ≈ 7.071067.
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, resulting in a wrong answer at the end of the sum. This may happen during subtraction or elsewhere.
Square Root of 1289 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1189?
The area of the square is approximately 1189 square units.
Explanation
The area of the square = side^2.
The side length is given as √1189.
Area of the square = side^2 = √1189 x √1189 = 34.495 x 34.495 ≈ 1189.
Therefore, the area of the square box is approximately 1189 square units.
Problem 2
A square-shaped building measuring 1289 square feet is built; if each of the sides is √1289, what will be the square feet of half of the building?
644.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1289 by 2 = 644.5.
So half of the building measures 644.5 square feet.
Problem 3
Calculate √1289 x 5.
179.4985
Explanation
The first step is to find the square root of 1289, which is approximately 35.90.
The second step is to multiply 35.90 by 5.
So, 35.90 x 5 = 179.4985.
Problem 4
What will be the square root of (1289 + 6)?
The square root is approximately 36.27.
Explanation
To find the square root, we need to find the sum of (1289 + 6). 1289 + 6 = 1295, and then √1295 ≈ 36.27.
Therefore, the square root of (1289 + 6) is approximately ±36.27.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1289 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 147.80 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1289 + 38) = 2 × (35.90 + 38) = 2 × 73.90 = 147.80 units.
FAQ on Square Root of 1289
1.What is √1289 in its simplest form?
2.Mention the factors of 1289.
3.Calculate the square of 1289.
4.Is 1289 a prime number?
5.1289 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 1289?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 1289?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 1289
- 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.
- Prime number: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
- 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.
- Long division method: A mathematical procedure used for dividing a large number by another number, used to find square roots of non-perfect squares.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
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Jaskaran Singh Saluja
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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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