119 LearnersLast updated on May 26th, 2025
Square Root of 641
If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The square root is used in fields such as engineering, physics, and finance. Here, we will discuss the square root of 641.
What is the Square Root of 641?
The square root is the inverse operation of squaring a number. 641 is not a perfect square. The square root of 641 can be expressed in both radical and exponential forms. In radical form, it is expressed as √641, whereas in exponential form, it is (641)^(1/2). The square root of 641 is approximately 25.31798, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 641
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like 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 641 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 641 is broken down into its prime factors:
Step 1: Finding the prime factors of 641 Since 641 is a prime number, it cannot be broken down into smaller prime factors.
Step 2: Since 641 is not a perfect square and is a prime number, calculating its square root using prime factorization is not applicable.
Square Root of 641 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we find the closest perfect square numbers for the given number. Let us now learn how to find the square root using the long-division method, step by step:
Step 1: Group the digits of 641 from right to left. In this case, we have 6 and 41.
Step 2: Find n such that n^2 is less than or equal to 6. The closest n is 2, since 2^2 = 4. Place 2 above the 6 as the first digit of the quotient.
Step 3: Subtract 4 from 6, and bring down 41 to form the new dividend 241.
Step 4: Double the current quotient (2), which is 4, and use it as the new divisor's first digit.
Step 5: Find a digit d such that (40 + d) * d ≤ 241. The value of d is 6, since 46 * 6 = 276, which is greater than 241, but 45 * 5 = 225, which is less than 241.
Step 6: Place 5 next to 2 in the quotient, making it 25. Subtract 225 from 241, leaving a remainder of 16.
Step 7: Bring down two zeros to form 1600 and continue the process to get a more accurate result.
Step 8: This process is continued until the desired precision is reached.
The square root of 641 is approximately 25.31.
Square Root of 641 by Approximation Method
The approximation method is an easy way to find the square roots of numbers, especially when they are not perfect squares. Let us learn how to find the square root of 641 using the approximation method:
Step 1: Identify the perfect squares closest to 641. The closest perfect squares are 625 (25^2) and 676 (26^2). √641 falls between 25 and 26.
Step 2: Apply the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Using the formula: (641 - 625) / (676 - 625) = 16 / 51 ≈ 0.314. Step 3: Add this decimal to the smaller integer, 25 + 0.314 = 25.314.
Thus, the approximate square root of 641 is 25.314.
Common Mistakes and How to Avoid Them in the Square Root of 641
Students often make mistakes while finding the square root, such as overlooking the negative square root. It's also common to skip steps in the long division method. Now, let us look at a few common mistakes 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 usually consider only the positive square root as it is often the required one.
For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.
Mistake 2
Not using the square root symbol properly
Not using the square root symbol properly is another mistake children make. It's important to first simplify the numbers inside the square root before moving on.
For example, √(12 + 24) ≠ √12 + √24. The correct simplification is √(12 + 24) = √36 = 6.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root to avoid mistakes in 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 to 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. Students might skip a step accidentally, leading to a wrong answer. This may happen during subtraction or elsewhere.
Square Root of 641 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √641?
The area of the square is 641 square units.
Explanation
The area of the square = side^2.
The side length is given as √641.
Area of the square = side^2 = √641 x √641 = 641.
Therefore, the area of the square box is 641 square units.
Problem 2
A square-shaped building measuring 641 square feet is built; if each of the sides is √641, what will be the square feet of half of the building?
320.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 641 by 2 gives us 320.5.
So half of the building measures 320.5 square feet.
Problem 3
Calculate √641 x 5.
126.5899
Explanation
The first step is to find the square root of 641, which is approximately 25.31798.
The second step is to multiply 25.31798 by 5.
So, 25.31798 x 5 ≈ 126.5899.
Problem 4
What will be the square root of (625 + 16)?
The square root is 26.
Explanation
To find the square root, we need to find the sum of (625 + 16).
625 + 16 = 641, and √641 ≈ 25.31798.
However, using the perfect squares, 625 + 16 = 641, where the closest perfect square is 676, √676 = 26.
Therefore, the square root of (625 + 16) is approximately 26.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √641 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 126.63596 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√641 + 38)
≈ 2 × (25.31798 + 38)
≈ 2 × 63.31798
≈ 126.63596 units.
FAQ on Square Root of 641
1.What is √641 in its simplest form?
2.Is 641 a prime number?
3.Calculate the square of 641.
4.What are the closest perfect squares to 641?
5.What is √641 rounded to two decimal places?
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 641?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 641?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 641
- Square root: A square root is the inverse operation of squaring a number. For example, 5^2 = 25, and the square root is √25 = 5.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction, such as √641.
- Principal square root: The principal square root is the non-negative square root of a number, often used in calculations.
- Prime number: A prime number has exactly two distinct positive divisors: 1 and itself. For example, 641 is a prime number.
- Long division method: A technique used to find the square root of a number by iteratively dividing and averaging.
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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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