124 LearnersLast updated on May 26th, 2025
Square Root of 4913
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 field of vehicle design, finance, etc. Here, we will discuss the square root of 4913.
What is the Square Root of 4913?
The square root is the inverse of the square of the number. 4913 is not a perfect square. The square root of 4913 is expressed in both radical and exponential form. In the radical form, it is expressed as √4913, whereas (4913)^(1/2) in exponential form. √4913 ≈ 70.07, 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 4913
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 method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 4913 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4913 is broken down into its prime factors.
Step 1: Finding the prime factors of 4913.
Breaking it down, we get 13 × 13 × 29: 13² × 29.
Step 2: Now we found out the prime factors of 4913. The second step is to make pairs of those prime factors. Since 4913 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 4913 using prime factorization is limited in finding an exact square root.
Square Root of 4913 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 4913, we need to group it as 13 and 49.
Step 2: Now we need to find n whose square is less than or equal to 49. We can say n is ‘7’ because 7 × 7 = 49. Now the quotient is 7, and after subtracting 49 - 49, the remainder is 0.
Step 3: Now let us bring down 13, which is the new dividend. Add the old divisor with the same number: 7 + 7 = 14, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 14n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 14n × n ≤ 1300. Consider n as 9, now 14 × 9 × 9 = 1134.
Step 6: Subtract 1300 from 1134; the difference is 166, and the quotient is 79.
Step 7: 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 16600.
Step 8: Now we need to find the new divisor that is 709 because 709 × 2 = 1418.
Step 9: Subtracting 1418 from 1660, we get the result 242.
Step 10: Now the quotient is 70.9.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.
So the square root of √4913 ≈ 70.07.
Square Root of 4913 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 4913 using the approximation method.
Step 1: Now we have to find the closest perfect square of √4913. The smallest perfect square less than 4913 is 4900 (70²), and the largest perfect square greater than 4913 is 5041 (71²). √4913 falls somewhere between 70 and 71.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (4913 - 4900) ÷ (5041 - 4900) = 0.07. 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 70 + 0.07 = 70.07, so the square root of 4913 is approximately 70.07.
Common Mistakes and How to Avoid Them in the Square Root of 4913
Students do make mistakes while finding the square root, like 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 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.
Mistake 2
Not adding square root symbol in proper places
Not using the square root 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 and then move on to the second step.
For example: √(12+24) = √12 + √24 is a wrong method of using roots.
The right way of using roots 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 approximate 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 keep away from 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, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square root of 4913 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4913?
The area of the square is 4913 square units.
Explanation
The area of the square = side².
The side length is given as √4913.
Area of the square = side² = √4913 × √4913 = 4913.
Therefore, the area of the square box is 4913 square units.
Problem 2
A square-shaped building measuring 4913 square feet is built; if each of the sides is √4913, what will be the square feet of half of the building?
2456.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 4913 by 2 = we get 2456.5.
So half of the building measures 2456.5 square feet.
Problem 3
Calculate √4913 × 5.
350.35
Explanation
The first step is to find the square root of 4913, which is approximately 70.07, the second step is to multiply 70.07 with 5.
So 70.07 × 5 ≈ 350.35.
Problem 4
What will be the square root of (2400 + 2513)?
The square root is approximately 70.07.
Explanation
To find the square root, we need to find the sum of (2400 + 2513). 2400 + 2513 = 4913, and then √4913 ≈ 70.07.
Therefore, the square root of (2400 + 2513) is approximately 70.07.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √4913 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 240.14 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√4913 + 50) = 2 × (70.07 + 50) = 2 × 120.07 ≈ 240.14 units.
FAQ on Square Root of 4913
1.What is √4913 in its simplest form?
2.Mention the factors of 4913.
3.Calculate the square of 4913.
4.Is 4913 a prime number?
5.4913 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 4913?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 4913?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 4913
- 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.
- Perfect square: A perfect square is a number that is the square of an integer. For example: 9, 16, and 25 are perfect squares.
- 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.
- Long division method: A method used to find the square root of numbers, especially non-perfect squares, by dividing and finding remainders step by step.
- Approximation method: A method used to find an approximate value of the square root by comparing it with nearby perfect squares.
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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
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