122 LearnersLast updated on May 26th, 2025
Square Root of 2113
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 various fields such as engineering, finance, etc. Here, we will discuss the square root of 2113.
What is the Square Root of 2113?
The square root is the inverse of the square of a number. 2113 is not a perfect square. The square root of 2113 is expressed in both radical and exponential forms. In the radical form, it is expressed as √2113, whereas in exponential form it is expressed as (2113)^(1/2). √2113 ≈ 45.973, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 2113
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods such as long division and approximation are used. Let us now explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2113 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2113 can be broken down into its prime factors.
Step 1: Finding the prime factors of 2113 2113 is a prime number itself, which means it cannot be broken down into smaller prime factors. Since 2113 is not a perfect square, calculation using prime factorization is impossible.
Square Root of 2113 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 2113, we need to group it as 13 and 21.
Step 2: Now we need to find n whose square is ≤ 21. We can say n is ‘4’ because 4 × 4 = 16, which is less than 21. Now the quotient is 4 after subtracting 21 - 16, the remainder is 5.
Step 3: Now let us bring down 13, which is the new dividend. Add the old divisor with the same number 4 + 4 to get 8, which will be our new divisor.
Step 4: The new divisor will be 8n. Now we need to find the value of n where 8n × n ≤ 513.
Step 5: The next step is finding a suitable n such that 8n × n ≤ 513. We find n is 5 because 85 × 5 = 425.
Step 6: Subtract 425 from 513, the difference is 88, and the quotient is 45.
Step 7: Since the new 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 8800.
Step 8: Multiply the new quotient by 2 (45 × 2 = 90), add a placeholder for n, making it 900n, then find n where 900n × n ≤ 8800. We find n is 9 because 909 × 9 = 8181.
Step 9: Subtracting 8181 from 8800, we get the result 619.
Step 10: The quotient is now 45.9.
Step 11: Continue these steps until we get two numbers after the decimal point. Continue until the remainder is zero or until the desired precision is achieved.
So the square root of √2113 is approximately 45.97.
Square Root of 2113 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 2113 using the approximation method.
Step 1: Find the closest perfect squares to √2113. The smallest perfect square less than 2113 is 2025, and the largest perfect square more than 2113 is 2209. √2113 falls somewhere between 45 and 47.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Largest perfect square - smallest perfect square) Using the formula (2113 - 2025) / (2209 - 2025) = 88 / 184 ≈ 0.478
Using the formula, we identified the decimal point of our square root. The next step is adding the integer part to the decimal number, which is 45 + 0.478 ≈ 45.97, so the square root of 2113 is approximately 45.97.
Common Mistakes and How to Avoid Them in the Square Root of 2113
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of these mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to be aware that a number does have both positive and negative square roots. However, we typically consider only the positive square root for practical purposes.
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 common mistake. Students should be taught to simplify the numbers inside the square root before proceeding to the next steps.
For Example: √(12 + 24) ≠ √12 + √24. The correct approach is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
Students should be taught to simplify numbers inside the square root to avoid mistakes when identifying approximate values.
For Example: √50 ≠ 7; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students should be taught the difference between cube root and square root to prevent 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, resulting in a wrong answer. This may occur during subtraction or in other steps.
Square Root of 2113 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2113?
The area of the square is approximately 2113 square units.
Explanation
The area of the square = side².
The side length is given as √2113.
Area of the square = side² = √2113 × √2113 = 2113.
Therefore, the area of the square box is approximately 2113 square units.
Problem 2
A square-shaped garden measures 2113 square feet. If each of the sides is √2113, what will be the square feet of half of the garden?
1056.5 square feet
Explanation
We can divide the given area by 2, as the garden is square-shaped.
Dividing 2113 by 2 = 1056.5.
So half of the garden measures 1056.5 square feet.
Problem 3
Calculate √2113 × 5.
Approximately 229.865
Explanation
The first step is to find the square root of 2113, which is approximately 45.973.
Then multiply 45.973 by 5.
So 45.973 × 5 ≈ 229.865.
Problem 4
What will be the square root of (2113 + 6)?
The square root is approximately 46.07
Explanation
To find the square root, we need to find the sum of (2113 + 6). 2113 + 6 = 2119, and then √2119 ≈ 46.07.
Therefore, the square root of (2113 + 6) is approximately ±46.07.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2113 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 167.946 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2113 + 38) = 2 × (45.973 + 38) = 2 × 83.973 = 167.946 units.
FAQ on Square Root of 2113
1.What is √2113 in its simplest form?
2.What are the factors of 2113?
3.What is the square of 2113?
4.Is 2113 a prime number?
5.What numbers is 2113 divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 2113?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 2113?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 2113
- 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 as a simple fraction, meaning it cannot be expressed as p/q, where p and q are integers, and q ≠ 0.
- Prime number: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Example: 2113.
- Long division method: A method used to find the square root of non-perfect squares by breaking down the process into a series of steps involving division and averaging.
- Approximation: A method of finding an approximate value for a mathematical expression, often used when calculating square roots of non-perfect squares.
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About BrightChamps in Singapore
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.
