120 LearnersLast updated on May 26th, 2025
Square Root of 2064
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 2064.
What is the Square Root of 2064?
The square root is the inverse of the square of a number. 2064 is not a perfect square. The square root of 2064 is expressed in both radical and exponential form. In the radical form, it is expressed as √2064, whereas (2064)^(1/2) in the exponential form. √2064 ≈ 45.433, 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 2064
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 2064 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2064 is broken down into its prime factors.
Step 1: Finding the prime factors of 2064
Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 7 x 7: 2^3 x 3^2 x 7^2
Step 2: Now we found out the prime factors of 2064. The second step is to make pairs of those prime factors. Since 2064 is not a perfect square, therefore the digits of the number can’t be grouped in complete pairs. Therefore, calculating √2064 using prime factorization gives us an approximate value since it contains unpaired factors.
Square Root of 2064 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 2064, we need to group it as 64 and 20.
Step 2: Now we need to find n whose square is less than or equal to 20. We can say n as ‘4’ because 4 x 4 is equal to 16, which is less than 20. Now the quotient is 4, after subtracting 16 from 20 the remainder is 4.
Step 3: Now let us bring down 64, which is the new dividend. Add the old divisor with the same number: 4 + 4 equals 8, which will be our new divisor.
Step 4: The new divisor will be 8n. We need to find the value of n.
Step 5: The next step is finding 8n x n ≤ 464. Let us consider n as 5, now 85 x 5 = 425.
Step 6: Subtract 425 from 464, the difference is 39, and the quotient is 45.
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 3900.
Step 8: Now we need to find the new divisor by considering a number for n that satisfies 900n x n ≤ 3900.
Step 9: Through approximation, we find n, and continue the process to get the square root up to the desired decimal places.
So the square root of √2064 is approximately 45.433.
Square Root of 2064 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 2064 using the approximation method.
Step 1: Now we have to find the closest perfect square of √2064. The smallest perfect square less than 2064 is 2025 and the largest perfect square greater than 2064 is 2116. √2064 falls somewhere between 45 and 46.
Step 2: Now we need to apply the formula that is: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula: (2064 - 2025) / (2116 - 2025) = 39 / 91 ≈ 0.428
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 45 + 0.428 = 45.428, so the square root of 2064 is approximately 45.428.
Common Mistakes and How to Avoid Them in the Square Root of 2064
Students do make mistakes while finding the square root, like forgetting about the negative square root or 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 the 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 the 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 simplify 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 ≈ 7.071067.
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 2064 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2064?
The area of the square is approximately 2064 square units.
Explanation
The area of the square = side^2.
The side length is given as √2064.
Area of the square = (√2064) x (√2064) = 2064.
Therefore, the area of the square box is approximately 2064 square units.
Problem 2
A square-shaped building measuring 2064 square feet is built; if each of the sides is √2064, what will be the square feet of half of the building?
1032 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2064 by 2, we get 1032.
So half of the building measures 1032 square feet.
Problem 3
Calculate √2064 x 5.
Approximately 227.165
Explanation
The first step is to find the square root of 2064, which is approximately 45.433.
The second step is to multiply 45.433 with 5.
So, 45.433 x 5 ≈ 227.165.
Problem 4
What will be the square root of (1032 + 1032)?
The square root is approximately 45.433.
Explanation
To find the square root, we need to find the sum of (1032 + 1032), which equals 2064. Then √2064 ≈ 45.433.
Therefore, the square root of (1032 + 1032) is approximately ±45.433.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2064 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 166.866 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2064 + 38) ≈ 2 × (45.433 + 38) ≈ 2 × 83.433 ≈ 166.866 units.
FAQ on Square Root of 2064
1.What is √2064 in its simplest form?
2.Mention the factors of 2064.
3.Calculate the square of 2064.
4.Is 2064 a prime number?
5.2064 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 2064?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 2064?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 2064
- 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that is more prominent due to its uses in the real world. That is the reason it is also known as the principal square root.
- Prime factorization: Prime factorization is breaking a number down into the set of prime numbers which multiply together to give the original number.
- Approximation: Approximation is a method of finding a value that is close enough to the correct answer, usually with some thought or calculation.
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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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