117 LearnersLast updated on May 26th, 2025
Square Root of 841
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 841.
What is the Square Root of 841?
The square root is the inverse of the square of the number. 841 is a perfect square. The square root of 841 is expressed in both radical and exponential form. In the radical form, it is expressed as √841, whereas (841)^(1/2) in the exponential form. √841 = 29, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 841
The prime factorization method can be used for perfect square numbers. For non-perfect square numbers, 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 841 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 841 is broken down into its prime factors.
Step 1: Finding the prime factors of 841 Breaking it down, we get 29 x 29: 29^2
Step 2: Now we found out the prime factors of 841. The second step is to make pairs of those prime factors. Since 841 is a perfect square, we can group the digits in pairs and find the square root.
Therefore, √841 = 29.
Square Root of 841 by Long Division Method
The long division method can be used for both perfect and 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 pair the numbers from right to left. In the case of 841, we need to pair it as 8 and 41.
Step 2: Now we need to find n whose square is less than or equal to 8. We can take n as ‘2’ because 2 x 2 = 4, which is less than 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.
Step 3: Bring down 41, making the new dividend 441. Add the old divisor with the same number 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be written as 4n. We need to find the value of n.
Step 5: The next step is finding 4n x n ≤ 441. Let us consider n as 9, now 49 x 9 = 441
Step 6: Subtract 441 from 441, and the remainder is 0, with the quotient as 29.
So the square root of √841 is 29.
Square Root of 841 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 approximate the square root of 841.
Step 1: We need to find the closest perfect squares around √841. The perfect squares closest to 841 are 784 (28^2) and 900 (30^2). √841 falls exactly between 28 and 30.
Step 2: Since 841 is a perfect square, we know that √841 = 29 exactly. Therefore, the square root of 841 is 29.
Common Mistakes and How to Avoid Them in the Square Root of 841
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping methods like long division. 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: √841 = 29, there is also -29 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 before moving to the next step.
For Example: √(9+16) ≠ √9 + √16. The correct way is √(9+16) = √25 = 5.
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 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between the cube root and square root constantly, as this will help them avoid mistakes.
For Example: √27 and ∛27 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 841 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √841?
The area of the square is 841 square units.
Explanation
The area of the square = side^2.
The side length is given as √841.
Area of the square = side^2 = √841 x √841 = 29 x 29 = 841.
Therefore, the area of the square box is 841 square units.
Problem 2
A square-shaped building measuring 841 square feet is built. If each of the sides is √841, what will be the square feet of half of the building?
420.5 square feet
Explanation
We can divide the given area by 2 as the building is square-shaped.
Dividing 841 by 2 = we get 420.5
So half of the building measures 420.5 square feet.
Problem 3
Calculate √841 x 5.
145
Explanation
The first step is to find the square root of 841, which is 29.
The second step is to multiply 29 with 5.
So 29 x 5 = 145.
Problem 4
What will be the square root of (841 + 0)?
The square root is 29.
Explanation
To find the square root, we need to find the sum of (841 + 0). 841 + 0 = 841, and then √841 = 29.
Therefore, the square root of (841 + 0) is ±29.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √841 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 134 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√841 + 38) = 2 × (29 + 38) = 2 × 67 = 134 units.
FAQ on Square Root of 841
1.What is √841 in its simplest form?
2.Mention the factors of 841.
3.Calculate the square of 841.
4.Is 841 a prime number?
5.841 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 841?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 841?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossary for the Square Root of 841
- Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse operation is the square root, so √16 = 4.
- Rational number: A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 841 is a perfect square because it is 29^2.
- Long division method: A method used to find the square root of a number by dividing the number into pairs of digits from right to left.
- Approximation method: An approach to find an approximate value of the square root by identifying two consecutive integers between which the square root lies.
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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.
