123 LearnersLast updated on May 26th, 2025
Square Root of 4633
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 4633.
What is the Square Root of 4633?
The square root is the inverse of the square of a number. 4633 is not a perfect square. The square root of 4633 is expressed in both radical and exponential form. In the radical form, it is expressed as √4633, whereas (4633)^(1/2) in the exponential form. √4633 ≈ 68.072, 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 4633
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 4633 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4633 is broken down into its prime factors.
Step 1: Finding the prime factors of 4633 Breaking it down, we find that 4633 = 13 x 357. Since 357 is also not a prime number, we break it down further into 3 x 119, and 119 into 7 x 17. Hence, the prime factorization of 4633 is 13 x 3 x 7 x 17.
Step 2: Since 4633 is not a perfect square, calculating its square root using prime factorization is not straightforward. We proceed with other methods.
Square Root of 4633 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 4633, we need to group it as 46 and 33.
Step 2: Now we need to find n whose square is less than or equal to 46. We choose n as ‘6’ because 6 x 6 = 36, which is less than 46. Now the quotient is 6, and after subtracting 36 from 46, the remainder is 10.
Step 3: Bring down 33, making the new dividend 1033. Double the quotient to get the new divisor, which is 12.
Step 4: Find a digit n such that 12n x n is less than or equal to 1033. We choose n as 8, because 128 x 8 = 1024, which is less than 1033.
Step 5: Subtract 1024 from 1033 to get a remainder of 9.
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 zeroes to the dividend. Now the new dividend is 900.
Step 7: Continue the process to find additional digits after the decimal point.
So the square root of √4633 ≈ 68.072
Square Root of 4633 by Approximation Method
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 4633 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √4633. The closest perfect squares to 4633 are 4624 (68^2) and 4761 (69^2). √4633 falls somewhere between 68 and 69.
Step 2: Now we need to apply the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Using the formula (4633 - 4624) / (4761 - 4624) = 9 / 137 ≈ 0.066. Adding this value to the smaller perfect square's root: 68 + 0.066 ≈ 68.066
So the square root of 4633 is approximately 68.072.
Common Mistakes and How to Avoid Them in the Square Root of 4633
Students make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in 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 the positive square root due to its practical 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. Teach children that simplifying the numbers inside the square root is important before moving 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 is to simplify the numbers inside the square root, which is crucial to avoid mistakes while identifying the approximate value.
For example, √50 ≠ 7; 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 the cube root and square root to avoid confusion.
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, and students might skip a step accidentally, leading to a wrong answer. This may happen during subtraction or elsewhere in the process.
Square Root of 4633 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4633?
The area of the square is approximately 4633 square units.
Explanation
The area of a square = side².
The side length is given as √4633.
Area of the square = (√4633)² = 4633.
Therefore, the area of the square box is 4633 square units.
Problem 2
A square-shaped field measuring 4633 square meters is built; if each of the sides is √4633, what will be the square meters of half of the field?
2316.5 square meters
Explanation
We can divide the given area by 2 as the field is square-shaped.
Dividing 4633 by 2 gives 2316.5.
So half of the field measures 2316.5 square meters.
Problem 3
Calculate √4633 x 5.
Approximately 340.36
Explanation
First, find the square root of 4633, which is approximately 68.072.
Then multiply 68.072 by 5.
So 68.072 x 5 ≈ 340.36.
Problem 4
What will be the square root of (4633 + 100)?
The square root is approximately 70.0357.
Explanation
First, find the sum of (4633 + 100), which equals 4733.
Then find the square root of 4733, which is approximately 70.0357.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √4633 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 236.144 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√4633 + 50) ≈ 2 × (68.072 + 50) = 2 × 118.072 = 236.144 units.
FAQ on Square Root of 4633
1.What is √4633 in its simplest form?
2.Mention the factors of 4633.
3.Calculate the square of 4633.
4.Is 4633 a prime number?
5.4633 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 4633?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 4633?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 4633
- Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, as 4 x 4 = 16.
- Irrational number: An irrational number cannot be written as a simple fraction, meaning its decimal form is non-repeating and non-terminating.
- Factorization: The process of breaking down a number into its constituent prime factors, such as breaking down 4633 into 13, 3, 7, and 17.
- Approximation: A numerical value close to the actual value, often used when the exact value cannot be easily calculated.
- Long division: A method used to divide larger numbers and to find square roots of non-perfect squares in a step-by-step manner.
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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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