103 LearnersLast updated on May 26th, 2025
Square Root of 4704
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 4704.
What is the Square Root of 4704?
The square root is the inverse of the square of the number. 4704 is not a perfect square. The square root of 4704 is expressed in both radical and exponential form. In the radical form, it is expressed as √4704, whereas (4704)^(1/2) in exponential form. √4704 ≈ 68.586, 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 4704
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers, 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 4704 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4704 is broken down into its prime factors.
Step 1: Finding the prime factors of 4704
Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 13: 2^5 x 3^3 x 13
Step 2: Now we have found the prime factors of 4704. The second step is to make pairs of those prime factors. Since 4704 is not a perfect square, the digits of the number can’t be grouped into pairs perfectly. Therefore, calculating √4704 using prime factorization requires approximation.
Square Root of 4704 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 4704, we need to group it as 04 and 47.
Step 2: Now we need to find n whose square is less than or equal to 47. We can say n is ‘6’ because 6 x 6 = 36, which is less than 47. Now the quotient is 6; after subtracting 36 from 47, the remainder is 11.
Step 3: Now let us bring down 04, which is the new dividend. Add the old divisor with the same number 6 + 6 = 12, which will be our new divisor.
Step 4: The new divisor will be 12n. We need to find the value of n such that 12n x n is less than or equal to 1104. Let us consider n as 9. Now 12 x 9 = 108, so 108 x 9 = 972.
Step 5: Subtract 972 from 1104; the difference is 132, and the quotient is 69.
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 13200.
Step 7: Now we need to find the new divisor as 138 because 1389 x 9 = 12501.
Step 8: Subtracting 12501 from 13200, we get the result 699.
Step 9: The quotient so far is 68.9.
Step 10: Continue these steps until we get two numbers after the decimal point.
So the square root of √4704 ≈ 68.59.
Square Root of 4704 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 4704 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √4704. The smallest perfect square less than 4704 is 4624 (68^2) and the largest perfect square more than 4704 is 4761 (69^2). √4704 falls somewhere between 68 and 69.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (4704 - 4624) / (4761 - 4624) = 0.58. Adding the result to the smaller perfect square's root gives us 68 + 0.58 = 68.58. Thus, the approximate square root of 4704 is 68.58.
Common Mistakes and How to Avoid Them in the Square Root of 4704
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Now let us look at a few of these 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 in most contexts.
For example: √50 = 7.07, but there is also -7.07, which should not be forgotten.
Square Root of 4704 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4704?
The area of the square is 4704 square units.
Explanation
The area of the square = side^2.
The side length is given as √4704.
Area of the square = side^2 = √4704 x √4704 = 4704.
Therefore, the area of the square box is 4704 square units.
Problem 2
A square-shaped field measuring 4704 square feet is built; if each of the sides is √4704, what will be the square feet of half of the field?
2352 square feet
Explanation
We can just divide the given area by 2 as the field is square-shaped.
Dividing 4704 by 2 gives us 2352.
So half of the field measures 2352 square feet.
Problem 3
Calculate √4704 x 5.
342.93
Explanation
The first step is to find the square root of 4704, which is approximately 68.59.
The second step is to multiply 68.59 by 5. 68.59 x 5 = 342.93
Problem 4
What will be the square root of (4761 - 57)?
The square root is 68.
Explanation
First, find the difference: 4761 - 57 = 4704.
Then, find the square root of 4704. √4704 ≈ 68.59
Hence, the approximate square root of (4761 - 57) is 68.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4704 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 213.18 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√4704 + 38) Perimeter = 2 × (68.59 + 38) ≈ 2 × 106.59 ≈ 213.18 units.
FAQ on Square Root of 4704
1.What is √4704 in its simplest form?
2.Mention the factors of 4704.
3.Calculate the square of 4704.
4.Is 4704 a prime number?
5.4704 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 4704?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 4704?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 4704
- 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; however, the positive square root is often used due to its applications in the real world. This is also known as the principal square root.
- Prime factorization: Breaking down a composite number into its prime factors. Example: 4704 = 2^5 x 3^3 x 13.
- Long division method: A technique used to find the square root of a number that is not a perfect square by dividing and averaging iteratively.
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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.
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