123 LearnersLast updated on May 26th, 2025
Square Root of 1148
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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 1148.
What is the Square Root of 1148?
The square root is the inverse of the square of a number. 1148 is not a perfect square. The square root of 1148 is expressed in both radical and exponential form. In radical form, it is expressed as √1148, whereas in exponential form, it is (1148)^(1/2). √1148 ≈ 33.873, 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 1148
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where 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 1148 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1148 is broken down into its prime factors:
Step 1: Finding the prime factors of 1148 Breaking it down, we get 2 × 2 × 287: 2^2 × 287
Step 2: Now we have found the prime factors of 1148. The second step is to make pairs of those prime factors. Since 1148 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √1148 using prime factorization is not straightforward.
Square Root of 1148 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, group the numbers from right to left. For 1148, group it as 14 and 11.
Step 2: Find n whose square is 11. We can say n is '3' because 3 × 3 = 9, which is less than or equal to 11. Now the quotient is 3. After subtracting 9 from 11, the remainder is 2.
Step 3: Bring down 48, which is the new dividend. Add the old divisor (3) to the same number (3) to 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: Find 6n × n ≤ 248. Let us consider n as 4, now 64 × 4 = 256, which is greater than 248, so we try n as 3.
Step 6: With n = 3, 63 × 3 = 189. Subtract 189 from 248, the difference is 59, and the quotient is 33.
Step 7: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 5900.
Step 8: Now find the new divisor. We use 678 × 8 = 5424.
Step 9: Subtracting 5424 from 5900 gives 476.
Step 10: The quotient is now 33.8.
Step 11: Continue these steps until we get two numbers after the decimal point. If there are no decimal values, continue till the remainder is zero. So the square root of √1148 is approximately 33.87.
Square Root of 1148 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 1148 using the approximation method.
Step 1: Find the closest perfect square of √1148. The smallest perfect square less than 1148 is 1089 (33^2), and the largest perfect square greater than 1148 is 1156 (34^2). √1148 falls somewhere between 33 and 34.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula, (1148 - 1089) ÷ (1156 - 1089) = 59 ÷ 67 = 0.88 Adding the value we got initially to the decimal number: 33 + 0.88 = 33.88. Therefore, the square root of 1148 is approximately 33.88.
Common Mistakes and How to Avoid Them in the Square Root of 1148
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few of these 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 generally use 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 additional calculations.
For example: √(12 + 24) = √12 + √24 is incorrect. 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 is incorrect; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be consistently reminded about the difference between cube roots and square roots to 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. Students might skip a step accidentally, which results in a wrong answer at the end. This may happen during subtraction or elsewhere in the process.
Square Root of 1148 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1148?
The area of the square is approximately 1318.63 square units.
Explanation
The area of the square = side^2.
The side length is given as √1148.
Area of the square = side^2 = √1148 × √1148 = 33.88 × 33.88 ≈ 1318.63
Therefore, the area of the square box is approximately 1318.63 square units.
Problem 2
A square-shaped building measuring 1148 square feet is built; if each of the sides is √1148, what will be the square feet of half of the building?
574 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1148 by 2 = 574
So, half of the building measures 574 square feet.
Problem 3
Calculate √1148 × 5.
169.4
Explanation
The first step is to find the square root of 1148, which is approximately 33.88.
The second step is to multiply 33.88 by 5.
So, 33.88 × 5 ≈ 169.4
Problem 4
What will be the square root of (1148 + 4)?
The square root is approximately 34.
Explanation
To find the square root, we need to find the sum of (1148 + 4). 1148 + 4 = 1152.
The square root of 1152 is approximately 34.
Therefore, the square root of (1148 + 4) is approximately ±34.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1148 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 143.76 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1148 + 38) = 2 × (33.88 + 38) = 2 × 71.88 ≈ 143.76 units.
FAQ on Square Root of 1148
1.What is √1148 in its simplest form?
2.Mention the factors of 1148.
3.Calculate the square of 1148.
4.Is 1148 a prime number?
5.1148 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 1148?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 1148?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 1148
- 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that is used in most real-world applications. This is known as the principal square root.
- Prime factorization: The expression of a number as the product of its prime factors.
- Decimal: A decimal is a number that contains a whole number and a fraction separated by a decimal point, such as 7.86, 8.65, and 9.42.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
