119 LearnersLast updated on May 26th, 2025
Square Root of 835
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 835.
What is the Square Root of 835?
The square root is the inverse of the square of the number. 835 is not a perfect square. The square root of 835 is expressed in both radical and exponential form. In the radical form, it is expressed as √835, whereas (835)^(1/2) in the exponential form. √835 ≈ 28.9026, 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 835
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 835 by Prime Factorization Method
The product of prime factors is the Prime factorization of a number. Now let us look at how 835 is broken down into its prime factors.
Step 1: Finding the prime factors of 835 Breaking it down, we get 5 x 167.
Step 2: Now we found out the prime factors of 835. Since 835 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 835 using prime factorization alone does not yield a perfect square root.
Square Root of 835 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 835, we need to group it as 35 and 8.
Step 2: Now we need to find n whose square is less than or equal to 8. We can say n is ‘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: Now let us bring down 35, which is the new dividend. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor in the form 4_.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we need to find n such that 4n x n ≤ 435. Let us consider n as 8, now 48 x 8 = 384.
Step 5: Subtract 384 from 435, the difference is 51, and the quotient is 28.
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 5100.
Step 7: Now we need to find the new divisor that fits into the dividend. Try 289 because 289 x 9 = 2601, which is less than 5100.
Step 8: Subtracting 2601 from 5100 we get the result 2499.
Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values continue till the remainder is zero.
So the square root of √835 is approximately 28.90.
Square Root of 835 by Approximation Method
The 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 835 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √835.
The smallest perfect square less than 835 is 784 (which is 28^2), and the largest perfect square greater than 835 is 841 (which is 29^2). √835 falls somewhere between 28 and 29.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (835 - 784) / (841 - 784) = 51 / 57 ≈ 0.8947.
Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the integer part which is 28 + 0.8947 ≈ 28.895, so the square root of 835 is approximately 28.90.
Common Mistakes and How to Avoid Them in the Square Root of 835
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 these 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 principal (positive) square root in most real-world applications.
For example: √50 ≈ 7.07, but 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 before moving on to the second step.
For example: √(12 + 24) ≠ √12 + √24. The right way of using roots 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 incorrect, 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 which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 835 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √835?
The area of the square is approximately 835 square units.
Explanation
The area of the square = side^2.
The side length is given as √835.
Area of the square = side^2 = (√835) x (√835) = 835.
Therefore, the area of the square box is approximately 835 square units.
Problem 2
A square-shaped building measuring 835 square feet is built; if each of the sides is √835, what will be the square feet of half of the building?
417.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 835 by 2 = we get 417.5.
So half of the building measures 417.5 square feet.
Problem 3
Calculate √835 x 5.
Approximately 144.51
Explanation
The first step is to find the square root of 835 which is approximately 28.90, the second step is to multiply 28.90 with 5. So 28.90 x 5 ≈ 144.51.
Problem 4
What will be the square root of (835 + 6)?
The square root is approximately 28.97
Explanation
To find the square root, we need to find the sum of (835 + 6). 835 + 6 = 841, and √841 = 29.
Therefore, the square root of (835 + 6) is ±29.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √835 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle is approximately 133.80 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√835 + 38) = 2 × (28.90 + 38) = 2 × 66.90 = 133.80 units.
FAQ on Square Root of 835
1.What is √835 in its simplest form?
2.Mention the factors of 835.
3.Calculate the square of 835.
4.Is 835 a prime number?
5.835 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 835?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 835?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 835
- 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 why it is also known as the principal square root.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 28 is 2 x 2 x 7.
- Long division method: A method used to find the square root of non-perfect squares, involving a series of divisions and subtractions to achieve an approximate value.
Explore More algebra
About BrightChamps in Indonesia
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.
