135 LearnersLast updated on May 26th, 2025
Square Root of 1009
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 1009
What is the Square Root of 1009?
The square root is the inverse of the square of the number. 1009 is not a perfect square. The square root of 1009 is expressed in both radical and exponential form. In the radical form, it is expressed as √1009, whereas (1009)^(1/2) in the exponential form. √1009 ≈ 31.76476, 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 1009
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 1009 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. However, 1009 is a prime number and cannot be broken down into smaller prime factors. Therefore, calculating 1009 using prime factorization is not applicable.
Square Root of 1009 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 1009, we need to group it as 09 and 10.
Step 2: Now we need to find n whose square is 10. We can approximate n as ‘3’ because 3^2 = 9 is lesser than or equal to 10. Now the quotient is 3 after subtracting 10 - 9 the remainder is 1.
Step 3: Now let us bring down 09 which is the new dividend. Add the old divisor with the same number 3 + 3 we get 6 which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 109 let us consider n as 1, now 61 x 1 = 61.
Step 6: Subtract 109 from 61; the difference is 48, and the quotient is 31.
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 4800.
Step 8: Now we need to find the new divisor that is 637 because 637 × 7 = 4459.
Step 9: Subtracting 4459 from 4800 we get the result 341.
Step 10: Now the quotient is 31.7.
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 √1009 is approximately 31.76.
Square Root of 1009 by Approximation Method
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 1009 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1009. The smallest perfect square less than 1009 is 961 (31^2) and the largest perfect square greater than 1009 is 1024 (32^2). √1009 falls somewhere between 31 and 32.
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 (1009 - 961) ÷ (1024 - 961) = 48 ÷ 63 ≈ 0.76. 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 31 + 0.76 = 31.76.
So the square root of 1009 is approximately 31.76.
Common Mistakes and How to Avoid Them in the Square Root of 1009
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: √1009 ≈ 31.76, there is also -31.76 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: √(10 + 9) ≠ √10 + √9. The right way of using roots is √(10 + 9) = √19.
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; 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 1009 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1009?
The area of the square is approximately 1009 square units.
Explanation
The area of the square = side^2.
The side length is given as √1009.
Area of the square = side^2
= √1009 × √1009
= 1009.
Therefore, the area of the square box is approximately 1009 square units.
Problem 2
A square-shaped building measuring 1009 square feet is built; if each of the sides is √1009, what will be the square feet of half of the building?
504.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1009 by 2 = 504.5
So half of the building measures 504.5 square feet.
Problem 3
Calculate √1009 × 5.
158.8238
Explanation
The first step is to find the square root of 1009 which is approximately 31.76476, the second step is to multiply 31.76476 with 5.
So 31.76476 × 5 ≈ 158.8238
Problem 4
What will be the square root of (1009 + 15)?
The square root is approximately 32.0312
Explanation
To find the square root, we need to find the sum of (1009 + 15) 1009 + 15 = 1024, and then √1024 = 32.
Therefore, the square root of (1009 + 15) is ±32.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1009 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 139.53 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1009 + 38)
≈ 2 × (31.76476 + 38)
= 2 × 69.76476
≈ 139.53 units.
FAQ on Square Root of 1009
1.What is √1009 in its simplest form?
2.Is 1009 a prime number?
3.What is the square of 1009?
4.Is 1009 a perfect square?
5.What is the decimal approximation of √1009?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 1009?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 1009?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 1009
- 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 has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Prime number: A prime number is a number greater than 1 that has no divisors other than 1 and itself.
- Decimal approximation: A decimal approximation is a method of finding a close decimal value of a non-integer result, often used for irrational numbers.
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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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