128 LearnersLast updated on May 26th, 2025
Square Root of 1145
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 architecture, engineering, and finance. Here, we will discuss the square root of 1145.
What is the Square Root of 1145?
The square root is the inverse of the square of a number. 1145 is not a perfect square. The square root of 1145 is expressed in both radical and exponential forms. In radical form, it is expressed as √1145, whereas (1145)^(1/2) in the exponential form. √1145 ≈ 33.829, 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 1145
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 1145 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1145 is broken down into its prime factors.
Step 1: Finding the prime factors of 1145 Breaking it down, we get 5 × 229: 5^1 × 229^1
Step 2: Now we found out the prime factors of 1145. Since 1145 is not a perfect square, the digits of the number can’t be grouped into pairs. Therefore, calculating 1145 using prime factorization is not feasible.
Square Root of 1145 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 1145, we need to group it as 11 and 45.
Step 2: Now we need to find n whose square is less than or equal to 11. We can say n is 3 because 3 × 3 = 9 is less than 11. Now the quotient is 3, and after subtracting 9 from 11, the remainder is 2.
Step 3: Now let us bring down 45, which is the new dividend. Add the old divisor with the same number 3 + 3, we 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 ≤ 245. Let us consider n as 4. Now 64 × 4 = 256 is greater than 245, so we try n as 3.
Step 6: With n = 3, 63 × 3 = 189. Subtract 245 from 189, and the difference is 56.
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 5600.
Step 8: Now we need to find the new divisor, which is 669 because 669 × 8 = 5352.
Step 9: Subtracting 5352 from 5600, we get the result 248.
Step 10: Now the quotient is 33.8.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero. So the square root of √1145 is approximately 33.82.
Square Root of 1145 by Approximation Method
The approximation method is another approach 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 1145 using the approximation method.
Step 1: Now we have to find the closest perfect square to √1145. The smallest perfect square less than 1145 is 1089, and the largest perfect square greater than 1145 is 1225. √1145 falls somewhere between 33 and 34.
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 (1145 - 1089) / (1225 - 1089) = 56 / 136 ≈ 0.4118. 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 33 + 0.4118 ≈ 33.82. So, the square root of 1145 is approximately 33.82.
Common Mistakes and How to Avoid Them in the Square Root of 1145
Students can make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in 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 has both positive and negative square roots. However, we typically take only the positive square root, as it is the required one in most real-world applications.
For example, √50 ≈ 7.07, but 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 symbol 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 moving on to the next step.
For example: √(12 + 24) = √36, not √12 + √24.
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 ≈ 7.071, not 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 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 calculation. This may happen in subtraction or elsewhere.
Square Root of 1145 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1145?
The area of the square is approximately 1145 square units.
Explanation
The area of the square = side^2.
The side length is given as √1145.
Area of the square = side^2 = √1145 × √1145 = 1145.
Therefore, the area of the square box is approximately 1145 square units.
Problem 2
A square-shaped plot measuring 1145 square feet is to be divided in half; if each of the sides is √1145, what will be the square feet of half of the plot?
572.5 square feet
Explanation
We can just divide the given area by 2 as the plot is square-shaped.
Dividing 1145 by 2 = 572.5
So half of the plot measures 572.5 square feet.
Problem 3
Calculate √1145 × 3.
Approximately 101.46
Explanation
The first step is to find the square root of 1145, which is approximately 33.82.
The second step is to multiply 33.82 by 3.
So, 33.82 × 3 = 101.46
Problem 4
What will be the square root of (1145 + 55)?
The square root is 35.
Explanation
To find the square root, we need to find the sum of (1145 + 55). 1145 + 55 = 1200, and then √1200 ≈ 34.64.
Therefore, the square root of (1145 + 55) is approximately 34.64.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √1145 units and the width 'w' is 50 units.
The perimeter of the rectangle is approximately 217.64 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1145 + 50) ≈ 2 × (33.82 + 50) ≈ 2 × 83.82 ≈ 167.64 units.
FAQ on Square Root of 1145
1.What is √1145 in its simplest form?
2.Mention the factors of 1145.
3.Calculate the square of 1145.
4.Is 1145 a prime number?
5.1145 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 1145?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 1145?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 1145
- 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.
- 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.
- Principal square root: A number has both positive and negative square roots, but it is always the positive square root that has more prominence due to its uses in the real world. This is why it is also known as the principal square root.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1145 is 5 × 229.
- Long division method: A step-by-step method for finding the square root of a non-perfect square number using division and subtraction.
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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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