129 LearnersLast updated on May 26th, 2025
Square Root of 1045
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 like engineering, finance, etc. Here, we will discuss the square root of 1045.
What is the Square Root of 1045?
The square root is the inverse of the square of the number. 1045 is not a perfect square. The square root of 1045 is expressed in both radical and exponential form. In the radical form, it is expressed as √1045, whereas (1045)^(1/2) in exponential form. √1045 ≈ 32.343, 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 1045
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 1045 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1045 is broken down into its prime factors.
Step 1: Finding the prime factors of 1045 Breaking it down, we get 5 × 11 × 19.
Step 2: We found the prime factors of 1045. Since 1045 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √1045 using prime factorization directly is not possible.
Square Root of 1045 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin, group the numbers from right to left. In the case of 1045, we need to group it as 10 and 45.
Step 2: Find a number whose square is less than or equal to 10. We can say this number is ‘3’ because 3 × 3 = 9. The quotient is 3, and the remainder is 1 after subtracting 9 from 10.
Step 3: Bring down the next pair, which is 45, making the new dividend 145. Add the old divisor with the same number, 3 + 3 = 6, to get the new divisor.
Step 4: The new divisor will be 6n. Find the largest value of n such that 6n × n ≤ 145. The value n is 2, so 62 × 2 = 124.
Step 5: Subtract 124 from 145, the result is 21, and the quotient is 32.
Step 6: Since the dividend is less than the divisor, add a decimal point. Add two zeroes to the dividend to make it 2100.
Step 7: The new divisor is 644. Find a number n such that 644n × n is less than or equal to 2100. Continue this process to achieve better precision.
So, the square root of √1045 is approximately 32.343.
Square Root of 1045 by Approximation Method
Approximation 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 1045 using the approximation method.
Step 1: Find the closest perfect squares of √1045. The smallest perfect square less than 1045 is 1024 (32^2), and the largest perfect square greater than 1045 is 1089 (33^2). √1045 falls between 32 and 33.
Step 2: Apply the approximation formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using (1045 - 1024) / (1089 - 1024) = 21 / 65 = 0.323.
The approximate square root is 32 + 0.323 = 32.323.
Common Mistakes and How to Avoid Them in the Square Root of 1045
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping the long division method. 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 has both positive and negative square roots. However, we typically use only the positive square root.
For example: √50 = 7.07, but there is also -7.07.
Mistake 2
Not adding the square root symbol in proper places
Improper use of the square root symbol is a common mistake. Teach students to simplify numbers inside the square root first.
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
Simplifying numbers inside the square root is crucial to avoid errors in approximating values.
For example: √50 ≠ 7; the correct value is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to understand the difference between cube root and square root.
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. Students might skip a step, leading to errors. This can occur in subtraction or other parts of the process.
Square Root of 1045 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1045?
The area of the square is approximately 1045 square units.
Explanation
The area of a square = side^2.
The side length is given as √1045.
Area = (√1045) × (√1045) = 1045.
Problem 2
A square-shaped building measuring 1045 square feet is built; if each side is √1045, what will be the square feet of half of the building?
522.5 square feet
Explanation
Divide the total area by 2 since the building is square-shaped.
1045 / 2 = 522.5 square feet.
Problem 3
Calculate √1045 × 3.
Approximately 97.029
Explanation
First, find the square root of 1045, which is approximately 32.343. Then multiply 32.343 by 3: 32.343 × 3 ≈ 97.029.
Problem 4
What will be the square root of (1024 + 21)?
The square root is 33.
Explanation
Find the sum of (1024 + 21) = 1045, then find the square root of 1045, which is approximately 32.343, but since this is a sum leading to a perfect square (1089), it simplifies to 33.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √1045 units and the width ‘w’ is 25 units.
The perimeter of the rectangle is approximately 114.686 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√1045 + 25)
= 2 × (32.343 + 25)
≈ 114.686 units.
FAQ on Square Root of 1045
1.What is √1045 in its simplest form?
2.Mention the factors of 1045.
3.Calculate the square of 1045.
4.Is 1045 a prime number?
5.1045 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 1045?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 1045?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 1045
- Square root: A square root is the inverse operation of squaring a number. For example, if 4^2 = 16, then √16 = 4.
- Irrational number: An irrational number cannot be expressed as a simple fraction; it has a non-repeating, non-terminating decimal expansion.
- Principal square root: The non-negative square root of a number. For example, the principal square root of 25 is 5.
- Factors: Numbers you can multiply together to get another number. For example, factors of 12 are 1, 2, 3, 4, 6, and 12.
- Perfect square: A number that is the square of an integer. For example, 36 is a perfect square because it is 6^2.
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About BrightChamps in Qatar
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.
