Last updated on May 26th, 2025
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.
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.
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:
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.
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
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.
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.
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.
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.
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
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.
Calculate √836 × 5.
144.54
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.
What will be the square root of (836 + 4)?
The square root is 29.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√836 + 20) = 2 × (28.91 + 20) = 2 × 48.91 ≈ 97.82 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.