102 LearnersLast updated on May 26th, 2025
Square Root of 1037
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 1037.
What is the Square Root of 1037?
The square root is the inverse of the square of the number. 1037 is not a perfect square. The square root of 1037 is expressed in both radical and exponential form. In the radical form, it is expressed as √1037, whereas (1037)^(1/2) in the exponential form. √1037 ≈ 32.2182, 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 1037
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 1037 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1037 is broken down into its prime factors.
Step 1: Finding the prime factors of 1037 Breaking it down, we find that 1037 is already a prime number. Thus, it cannot be simplified further into other prime factors.
Since 1037 is not a perfect square, calculating its square root using prime factorization is not feasible.
Square Root of 1037 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 1037, we need to group it as 37 and 10.
Step 2: Now we need to find n whose square is closest to 10. We can say n is '3' because 3×3 = 9 is lesser than 10. Now the quotient is 3, and after subtracting 9 from 10, the remainder is 1.
Step 3: Now let us bring down 37, making the new dividend 137. Add the old divisor with the same number: 3+3=6, which will be our new divisor.
Step 4: The new divisor is 6n. We need to find n such that 6n × n ≤ 137. Let us consider n as 2, now 62×2 = 124.
Step 5: Subtract 124 from 137, the difference is 13, and the quotient is 32.
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 1300.
Step 7: Now we need to find the new divisor, which is 644 because 644×2 = 1288.
Step 8: Subtracting 1288 from 1300, we get the result of 12.
Step 9: The quotient now is 32.2.
Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue until the remainder is zero.
So the square root of √1037 is approximately 32.218.
Square Root of 1037 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 1037 using the approximation method.
Step 1: Find the closest perfect squares of √1037. The smallest perfect square less than 1037 is 1024, and the largest perfect square greater than 1037 is 1089. √1037 falls somewhere between 32 and 33.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (1037 - 1024) / (1089 - 1024) = 13 / 65 ≈ 0.2 Using the formula, we identified the decimal point of our square root. Adding this to the initial value, we get 32 + 0.2 = 32.2.
Therefore, the square root of 1037 is approximately 32.218.
Common Mistakes and How to Avoid Them in the Square Root of 1037
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping the long division methods. 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 has 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.
Square Root of 1037 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1037?
The area of the square is approximately 1037 square units.
Explanation
The area of the square = side^2.
The side length is given as √1037.
Area of the square = side^2
= √1037 × √1037
≈ 1037
Therefore, the area of the square box is approximately 1037 square units.
Problem 2
A square-shaped garden measuring 1037 square meters is built. If each of the sides is √1037, what will be the square meters of half of the garden?
518.5 square meters
Explanation
We can divide the given area by 2 as the garden is square-shaped. Dividing 1037 by 2 = 518.5 So half of the garden measures 518.5 square meters.
Problem 3
Calculate √1037 × 5.
Approximately 161.091
Explanation
The first step is to find the square root of 1037, which is approximately 32.218.
The second step is to multiply 32.218 by 5.
So 32.218 × 5 ≈ 161.091
Problem 4
What will be the square root of (1037 + 13)?
The square root is approximately 32.496
Explanation
To find the square root, we need to find the sum of (1037 + 13).
1037 + 13 = 1050, and then √1050 ≈ 32.496.
Therefore, the square root of (1037 + 13) is approximately ±32.496.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √1037 units and the width 'w' is 40 units.
We find the perimeter of the rectangle as approximately 144.436 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1037 + 40)
≈ 2 × (32.218 + 40)
= 2 × 72.218
= 144.436 units.
FAQ on Square Root of 1037
1.What is √1037 in its simplest form?
2.Can 1037 be factored further?
3.Calculate the square of 1037.
4.Is 1037 a prime number?
5.What is the closest perfect square to 1037?
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 1037?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 1037?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 1037
- Square root: A square root is the inverse of squaring a number. For example, 4^2 = 16, and the square root of 16 is 4, written as √16 = 4.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction p/q, where q is not zero and p and q are integers.
- Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- Decimal: A decimal number contains a whole number and a fractional part separated by a decimal point, such as 7.86, 8.65, and 9.42.
- Approximation: In mathematics, an approximation is a value or quantity that is nearly but not exactly correct.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
