124 LearnersLast updated on May 26th, 2025
Square Root of 1233
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 1233.
What is the Square Root of 1233?
The square root is the inverse of the square of the number. 1233 is not a perfect square. The square root of 1233 is expressed in both radical and exponential form. In the radical form, it is expressed as √1233, whereas (1233)^(1/2) in the exponential form. √1233 ≈ 35.111, 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 1233
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 1233 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1233 is broken down into its prime factors:
Step 1: Finding the prime factors of 1233 Breaking it down, we get 3 x 3 x 137.
Step 2: Now we found out the prime factors of 1233. The second step is to make pairs of those prime factors. Since 1233 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 1233 using prime factorization for an exact square root is not possible.
Square Root of 1233 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 1233, we need to group it as 33 and 12.
Step 2: Now we need to find n whose square is ≤ 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 12 - 9 = 3.
Step 3: Now let us bring down 33, which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.
Step 4: The new divisor will be 6n. We need to find the value of n such that 6n x n ≤ 333. Let us consider n as 5, now 65 x 5 = 325.
Step 5: Subtract 325 from 333, the difference is 8, and the quotient becomes 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 zeros to the dividend. Now the new dividend is 800.
Step 7: Now we need to find the new divisor that is 701 because 701 x 1 = 701.
Step 8: Subtracting 701 from 800, we get the result 99.
Step 9: Now the quotient is 35.1.
Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue until the remainder is zero.
So the square root of √1233 is approximately 35.11.
Square Root of 1233 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 1233 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1233. The smallest perfect square less than 1233 is 1225 and the largest perfect square greater than 1233 is 1296. √1233 falls somewhere between 35 and 36.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (1233 - 1225) / (1296 - 1225) = 8 / 71 ≈ 0.113 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 35 + 0.113 ≈ 35.11, so the square root of 1233 is approximately 35.11.
Common Mistakes and How to Avoid Them in the Square Root of 1233
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, 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 has both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √50 ≈ 7.07, 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 children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before moving on to the second step.
For example, √(12 + 24) ≠ √12 + √24. The correct way 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 children 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 wrong; the correct answer is √50 ≈ 7.071.
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 in subtracting or elsewhere.
Square root of 1233 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1233?
The area of the square is approximately 1520.72 square units.
Explanation
The area of the square = side^2.
The side length is given as √1233.
Area of the square = (√1233)² = 1233.
Therefore, the area of the square box is approximately 1233 square units.
Problem 2
A square-shaped building measuring 1233 square feet is built; if each of the sides is √1233, what will be the square feet of half of the building?
616.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1233 by 2 gives us 616.5.
So half of the building measures 616.5 square feet.
Problem 3
Calculate √1233 x 5.
Approximately 175.555
Explanation
The first step is to find the square root of 1233 which is approximately 35.111.
The second step is to multiply 35.111 by 5.
So 35.111 x 5 ≈ 175.555.
Problem 4
What will be the square root of (1225 + 8)?
The square root is approximately 35.11
Explanation
To find the square root, we need to find the sum of (1225 + 8) = 1233, and then √1233 ≈ 35.11.
Therefore, the square root of (1225 + 8) is approximately ±35.11.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √1233 units and the width 'w' is 38 units.
The perimeter of the rectangle is approximately 146.222 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1233 + 38)
≈ 2 × (35.111 + 38)
≈ 2 × 73.111
= 146.222 units.
FAQ on Square Root of 1233
1.What is √1233 in its simplest form?
2.Mention the factors of 1233.
3.Calculate the square of 1233.
4.Is 1233 a prime number?
5.1233 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 1233?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 1233?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 1233
- 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 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 has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Perfect square: A perfect square is a number that is the square of an integer, such as 4, 9, 16, etc.
- Long division method: A technique used to find the square roots of non-perfect squares by grouping and long division.
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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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