120 LearnersLast updated on May 26th, 2025
Square Root of 836
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 836.
What is the Square Root of 836?
The square root is the inverse of the square of a number. 836 is not a perfect square. The square root of 836 is expressed in both radical and exponential form. In the radical form, it is expressed as √836, whereas in the exponential form it is expressed as (836)^(1/2). √836 ≈ 28.9087, 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 836
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 836 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 836 is broken down into its prime factors.
Step 1: Finding the prime factors of 836 Breaking it down, we get 2 x 2 x 11 x 19: 2^2 x 11^1 x 19^1
Step 2: Now we found the prime factors of 836. The second step is to make pairs of those prime factors. Since 836 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 836 using prime factorization alone to find its square root is not feasible.
Square Root of 836 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 836, we need to group it as 36 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 is less than or equal to 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.
Step 3: Now let us bring down 36, which is the new dividend. Add the old divisor with the same number 2 + 2; we get 4, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we need to find the value of n such that 4n x n is less than or equal to 436.
Step 5: Consider n as 8, now 4 x 8 x 8 = 256.
Step 6: Subtract 256 from 436, the difference is 180, and the quotient is 28.
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 18000.
Step 8: Now we need to find the new divisor that is 578 because 578 x 3 = 1734.
Step 9: Subtracting 1734 from 18000, we get the result 266.
Step 10: Now the quotient is 28.9
Step 11: Continue doing these steps until we get two numbers after the decimal point.
So the square root of √836 is approximately 28.90
Square Root of 836 by Approximation Method
The approximation method is another method for finding square roots, and 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 836 using the approximation method.
Step 1: Now we have to find the closest perfect square of √836.
The smallest perfect square less than 836 is 784, and the largest perfect square greater than 836 is 841. √836 falls somewhere between 28 and 29.
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 (836 - 784) / (841 - 784) = 52/57 ≈ 0.912.
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 28 + 0.912 = 28.912, so the square root of 836 is approximately 28.912.
Common Mistakes and How to Avoid Them in the Square Root of 836
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. 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 square root symbol in proper places
Not using the square root symbol properly is another mistake that students often make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving to the second step.
For Example: √(12+24) = √12 + √24 is an incorrect method of using roots. The correct 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 students 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, resulting in a wrong answer at the end of the sum. This may happen in subtraction or elsewhere.
Square Root of 836 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √836?
The area of the square is approximately 698.5 square units.
Explanation
The area of the square = side^2.
The side length is given as √836.
Area of the square = side^2 = √836 x √836 ≈ 28.91 × 28.91 ≈ 698.5.
Therefore, the area of the square box is approximately 698.5 square units.
Problem 2
A square-shaped garden measuring 836 square feet is planned; if each of the sides is √836, what will be the square feet of half of the garden?
418 square feet
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 836 by 2, we get 418.
So half of the garden measures 418 square feet.
Problem 3
Calculate √836 × 5.
144.54
Explanation
The first step is to find the square root of 836, which is approximately 28.91.
The second step is to multiply 28.91 by 5.
So, 28.91 × 5 ≈ 144.54.
Problem 4
What will be the square root of (836 + 4)?
The square root is 29.
Explanation
To find the square root, we need to find the sum of (836 + 4). 836 + 4 = 840, and then √840 ≈ 29.
Therefore, the square root of (836 + 4) is ±29.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √836 units and the width ‘w’ is 20 units.
The perimeter of the rectangle is approximately 97.82 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√836 + 20) = 2 × (28.91 + 20) = 2 × 48.91 ≈ 97.82 units.
FAQ on Square Root of 836
1.What is √836 in its simplest form?
2.Mention the factors of 836.
3.Calculate the square of 836.
4.Is 836 a prime number?
5.836 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 836?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 836?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 836
- 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.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Prime factorization: The process of expressing a number as a product of its prime factors.
- Long division method: A technique used to find the square root of non-perfect squares using a division-like process.
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Jaskaran Singh Saluja
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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.
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