100 LearnersLast updated on May 26th, 2025
Square Root of 4645
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 4645.
What is the Square Root of 4645?
The square root is the inverse of the square of the number. 4645 is not a perfect square. The square root of 4645 is expressed in both radical and exponential form. In radical form, it is expressed as √4645, whereas in exponential form it is (4645)^(1/2). √4645 ≈ 68.16, 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 4645
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like 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 4645 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4645 is broken down into its prime factors.
Step 1: Finding the prime factors of 4645 Breaking it down, we get 5 x 929. Since 929 is a prime number, 4645 = 5 x 929.
Step 2: Now we have found out the prime factors of 4645. The second step is to make pairs of those prime factors. Since 4645 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 4645 using prime factorization is impractical for finding the square root.
Square Root of 4645 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 4645, we look at the digits in pairs from right to left: 45 and 46.
Step 2: Now we need to find n whose square is ≤ 46. The largest such n is 6 because 6^2 = 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 45, making the new dividend 1045. Add the old divisor with the same number 6 + 6 = 12, which will be part of our new divisor.
Step 4: The new divisor is now 12n. We need to find the value of n such that 12n x n ≤ 1045.
Step 5: Testing n = 8, we get 128 x 8 = 1024.
Step 6: Subtract 1024 from 1045 to get the difference, which is 21. The quotient is now 68.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to bring down two zeroes to the dividend, making it 2100.
Step 8: We find the new divisor that is 136, because 1369 x 1 = 1369.
Step 9: Subtract 1369 from 2100 to get 731.
Step 10: Continue the process to get more decimal precision. The quotient is approximately 68.16.
Square Root of 4645 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 4645 using the approximation method.
Step 1: Now we have to find the closest perfect squares for √4645. The smallest perfect square less than 4645 is 4624 (68^2) and the largest perfect square greater than 4645 is 4761 (69^2). √4645 falls somewhere between 68 and 69.
Step 2: Now we apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (4645 - 4624) ÷ (4761 - 4624) = 21 ÷ 137 ≈ 0.153. Using the formula, we identified the decimal point for our square root. The next step is adding the value we got initially to the decimal number which is 68 + 0.153 = 68.153, so the square root of 4645 is approximately 68.153.
Common Mistakes and How to Avoid Them in the Square Root of 4645
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division steps, 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 does have 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.
Square Root of 4645 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4645?
The area of the square is approximately 215,620.25 square units.
Explanation
The area of the square = side^2.
The side length is given as √4645.
Area of the square = side^2 = √4645 x √4645 = 68.16 x 68.16 ≈ 215,620.25.
Therefore, the area of the square box is approximately 215,620.25 square units.
Problem 2
A square-shaped building measuring 4645 square feet is built; if each of the sides is √4645, what will be the square feet of half of the building?
2322.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 4645 by 2 gives us 2322.5.
So half of the building measures 2322.5 square feet.
Problem 3
Calculate √4645 x 5.
Approximately 340.8
Explanation
The first step is to find the square root of 4645, which is approximately 68.16.
The second step is to multiply 68.16 with 5.
So 68.16 x 5 ≈ 340.8.
Problem 4
What will be the square root of (4625 + 20)?
The square root is approximately 68.
Explanation
To find the square root, we need to find the sum of (4625 + 20). 4625 + 20 = 4645, and then √4645 ≈ 68.153.
Therefore, the square root of (4625 + 20) is approximately ±68.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4645 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 212.32 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4645 + 38) = 2 × (68.16 + 38) = 2 × 106.16 = 212.32 units.
FAQ on Square Root of 4645
1.What is √4645 in its simplest form?
2.Mention the factors of 4645.
3.Calculate the square of 4645.
4.Is 4645 a prime number?
5.4645 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 4645?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 4645?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 4645
- 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.
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.
- Long division method: A technique used to find the square root of a number by dividing it step-by-step to get an approximate value.
- Decimal: If a number has a whole number and a fraction in a single representation, it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
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About BrightChamps in Oman
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.
