124 LearnersLast updated on May 26th, 2025
Square Root of 6409
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 6409.
What is the Square Root of 6409?
The square root is the inverse of the square of the number. 6409 is not a perfect square. The square root of 6409 is expressed in both radical and exponential form. In the radical form, it is expressed as √6409, whereas (6409)^(1/2) in the exponential form. √6409 ≈ 80.0587, 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 6409
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 6409 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 6409 is broken down into its prime factors.
Step 1: Finding the prime factors of 6409 Breaking it down, we find that 6409 is not easily broken down into smaller prime factors.
Step 2: Since 6409 is not a perfect square, calculating 6409 using the prime factorization method is not straightforward.
Square Root of 6409 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 6409, we need to group it as 64 and 09.
Step 2: Now we need to find n whose square is 64. We can say n as ‘8’ because 8 × 8 = 64. Now the quotient is 8, and after subtracting 64 from 64, the remainder is 0.
Step 3: Now let us bring down 09, which is the new dividend. Double the old divisor 8, which gives us 16 as our new divisor.
Step 4: Find n such that 16n × n ≤ 09. We can say n = 0, because 160 × 0 = 0.
Step 5: The quotient is 80.
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 900.
Step 7: Now we need to find the new divisor, 160, which gives us 1600 × 0 ≤ 900.
Step 8: Continue doing these steps until we get two numbers after the decimal point.
So the square root of √6409 is approximately 80.06.
Square Root of 6409 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 6409 using the approximation method.
Step 1: Now we have to find the closest perfect square of √6409.
The smallest perfect square less than 6409 is 6400, and the largest perfect square greater than 6409 is 6561. √6409 falls somewhere between 80 and 81.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Going by the formula (6409 - 6400) ÷ (6561 - 6400) ≈ 0.0587.
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 80 + 0.0587 ≈ 80.06.
So the square root of 6409 is approximately 80.06.
Common Mistakes and How to Avoid Them in the Square Root of 6409
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 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 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 avoid 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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 6409 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4096?
The area of the square is 4096 square units.
Explanation
The area of the square = side².
The side length is given as √4096.
Area of the square = side² = √4096 × √4096 = 64 × 64 = 4096.
Therefore, the area of the square box is 4096 square units.
Problem 2
A square-shaped garden measuring 6409 square feet is built; if each of the sides is √6409, what will be the square feet of half of the garden?
3204.5 square feet
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 6409 by 2 = we get 3204.5.
So half of the garden measures 3204.5 square feet.
Problem 3
Calculate √6409 × 10.
800.587
Explanation
The first step is to find the square root of 6409, which is 80.0587.
The second step is to multiply 80.0587 with 10.
So 80.0587 × 10 = 800.587.
Problem 4
What will be the square root of (6400 + 9)?
The square root is 80.06.
Explanation
To find the square root, we need to find the sum of (6400 + 9). 6400 + 9 = 6409, and then √6409 ≈ 80.06.
Therefore, the square root of (6400 + 9) is approximately ±80.06.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √6409 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as 260.12 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√6409 + 50) = 2 × (80.06 + 50) = 2 × 130.06 = 260.12 units.
FAQ on Square Root of 6409
1.What is √6409 in its simplest form?
2.Mention the factors of 6409.
3.Calculate the square of 6409.
4.Is 6409 a prime number?
5.6409 is 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 6409?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 6409?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 6409
- 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 the principal square root.
- Long division method: A method used to find the square roots of non-perfect squares using division steps to approximate the root.
- Approximation method: A method used to estimate the square root of a non-perfect square by finding the closest 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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