125 LearnersLast updated on May 26th, 2025
Square Root of 1049
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 1049.
What is the Square Root of 1049?
The square root is the inverse of the square of the number. 1049 is not a perfect square. The square root of 1049 is expressed in both radical and exponential form. In the radical form, it is expressed as √1049, whereas 1049^(1/2) in the exponential form. √1049 ≈ 32.407, 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 1049
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 method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1049 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1049 is broken down into its prime factors.
Step 1: Finding the prime factors of 1049. Since 1049 is a prime number itself, it cannot be broken down into smaller prime factors other than 1049 and 1.
Step 2: Since 1049 is not a perfect square, therefore, calculating 1049 using prime factorization to find its square root directly is not feasible.
Square Root of 1049 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: Group the digits in pairs from right to left. In the case of 1049, it is already a four-digit number, so we consider it as 10|49.
Step 2: Find a number whose square is less than or equal to the first group (10). The number is 3 because 3^2 = 9.
Step 3: Subtract 9 from 10, leaving a remainder of 1. Bring down the next group of digits (49) to make the new dividend 149.
Step 4: The new divisor is twice the current quotient (3), which gives us 6. We need to find a digit n such that 6n × n ≤ 149.
Step 5: n = 2 fits because 62 × 2 = 124.
Step 6: Subtract 124 from 149 to get a remainder of 25. Now, bring down double zeros to make it 2500.
Step 7: Continue this process to find the next digits of the square root, adding a decimal point as necessary.
After several iterations, the square root of 1049 is approximately 32.407.
Square Root of 1049 by Approximation Method
The approximation method is another method for finding the 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 1049 using the approximation method.
Step 1: Find the closest perfect squares around 1049. The closest perfect square less than 1049 is 1024 (32^2), and the one greater is 1089 (33^2).
Step 2: Since 1049 is closer to 1024, we estimate that the square root of 1049 is slightly more than 32 but less than 33. Using linear approximation, we can find a more precise value.
Common Mistakes and How to Avoid Them in the Square Root of 1049
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods like long division. Let us look at a few common mistakes 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 focus on the positive square root in practical applications.
For example, √1049 ≈ 32.407, but there is also -32.407, which should not be ignored in theoretical contexts.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake. To resolve this, we need to teach students the importance of simplifying numbers inside the square root before proceeding to further calculations.
For example, √(16 + 9) is not equal to √16 + √9.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught is simplifying numbers inside the square root, ensuring accurate approximations.
For example, √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students often confuse the square root and cube root symbols. It's crucial to distinguish between them.
For example, √8 and ∛8 are not the same.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps, which can lead to errors if steps are skipped. This may occur in subtraction or other parts of the process.
Square Root of 1049 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1049?
The area of the square is approximately 1049 square units.
Explanation
The area of the square = side².
The side length is given as √1049.
Area of the square = side²
= (√1049) × (√1049)
= 1049.
Therefore, the area of the square box is approximately 1049 square units.
Problem 2
A square-shaped building measuring 1049 square feet is built; if each of the sides is √1049, what will be the square feet of half of the building?
524.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1049 by 2 gives us 524.5.
So half of the building measures 524.5 square feet.
Problem 3
Calculate √1049 × 5.
Approximately 162.035
Explanation
First, find the square root of 1049, which is approximately 32.407.
Then, multiply 32.407 by 5. So, 32.407 × 5 ≈ 162.035.
Problem 4
What will be the square root of (1000 + 49)?
The square root is approximately 32.407.
Explanation
To find the square root, calculate the sum of (1000 + 49) which equals 1049.
Then, the square root of 1049 is approximately 32.407.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √1049 units and the width 'w' is 38 units.
The perimeter of the rectangle is approximately 140.814 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1049 + 38)
≈ 2 × (32.407 + 38)
= 2 × 70.407
= 140.814 units.
FAQ on Square Root of 1049
1.What is √1049 in its simplest form?
2.Is 1049 a perfect square?
3.Calculate the square of 1049.
4.Is 1049 a prime number?
5.1049 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 1049?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 1049?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 1049
- 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 cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Prime number: A prime number is a natural number greater than 1 that has no divisors other than 1 and itself.
- Approximation method: A method used to estimate the square root of non-perfect squares by determining nearby perfect squares.
- Long division method: A step-by-step process used to find the square root of non-perfect squares, involving repeated division and averaging.
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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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