121 LearnersLast updated on May 26th, 2025
Square Root of 2057
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 2057.
What is the Square Root of 2057?
The square root is the inverse of the square of the number. 2057 is not a perfect square. The square root of 2057 is expressed in both radical and exponential form. In the radical form, it is expressed as √2057, whereas (2057)^(1/2) in exponential form. √2057 ≈ 45.342, 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 2057
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 2057 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2057 is broken down into its prime factors.
Step 1: Finding the prime factors of 2057
Breaking it down, we get 2057 = 11 x 11 x 17.
Step 2: Now we have found the prime factors of 2057. The second step is to make pairs of those prime factors. Since 2057 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 2057 using prime factorization is impossible.
Square Root of 2057 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 2057, we group it as 57 and 20.
Step 2: Now we need to find n whose square is ≤ 20. We can say n as ‘4’ because 4 x 4 = 16 and is lesser than or equal to 20. Now the quotient is 4; after subtracting 16 from 20, the remainder is 4.
Step 3: Now let us bring down 57, which is the new dividend. Add the old divisor, 4, with the same number 4 + 4, we get 8, which will be our new divisor.
Step 4: The new divisor is 8, and we need to find n such that 8n x n ≤ 457. Let us consider n as 5, now 85 x 5 = 425.
Step 5: Subtract 425 from 457, the difference is 32, and the quotient is 45.
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 3200.
Step 7: Now we need to find the new divisor that is 453 because 453 x 7 = 3171.
Step 8: Subtracting 3171 from 3200, we get the result 29.
Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.
So the square root of √2057 is approximately 45.34.
Square Root of 2057 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 2057 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √2057. The smallest perfect square less than 2057 is 2025, and the largest perfect square greater than 2057 is 2116. √2057 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 (2057 - 2025) / (2116 - 2025) = 32 / 91 ≈ 0.35.
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 + 0.35 = 45.35. So the square root of 2057 is approximately 45.35.
Common Mistakes and How to Avoid Them in the Square Root of 2057
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 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 2057 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2057?
The area of the square is 2057 square units.
Explanation
The area of the square = side².
The side length is given as √2057.
Area of the square = side² = √2057 x √2057 = 2057.
Therefore, the area of the square box is 2057 square units.
Problem 2
A square-shaped building measuring 2057 square feet is built; if each of the sides is √2057, what will be the square feet of half of the building?
1028.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 2057 by 2 = we get 1028.5.
So half of the building measures 1028.5 square feet.
Problem 3
Calculate √2057 x 3.
136.03
Explanation
The first step is to find the square root of 2057, which is approximately 45.34.
The second step is to multiply 45.34 by 3.
So 45.34 x 3 ≈ 136.03.
Problem 4
What will be the square root of (2025 + 32)?
The square root is approximately 45.35.
Explanation
To find the square root, we need to find the sum of (2025 + 32). 2025 + 32 = 2057, and then √2057 ≈ 45.35.
Therefore, the square root of (2025 + 32) is approximately ±45.35.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2057 units and the width ‘w’ is 25 units.
We find the perimeter of the rectangle as 140.68 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2057 + 25) = 2 × (45.34 + 25) = 2 × 70.34 = 140.68 units.
FAQ on Square Root of 2057
1.What is √2057 in its simplest form?
2.Mention the factors of 2057.
3.Calculate the square of 2057.
4.Is 2057 a prime number?
5.2057 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 2057?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 2057?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 2057
- 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 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 has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 49 is a perfect square because it is 7².
- Long division method: A technique used to divide larger numbers by finding the quotient and remainder systematically, often applied to find square roots of non-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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