Last updated on May 26th, 2025
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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 8836.
The square root is the inverse of the square of a number. 8836 is a perfect square. The square root of 8836 is expressed in both radical and exponential form. In the radical form, it is expressed as √8836, whereas (8836)^(1/2) in the exponential form. √8836 = 94, 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.
The prime factorization method is used for perfect square numbers. For non-perfect square numbers, long-division and approximation methods 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 8836 is broken down into its prime factors:
Step 1: Finding the prime factors of 8836
Breaking it down, we get 2 x 2 x 47 x 47: 2^2 x 47^2
Step 2: Now we found out the prime factors of 8836. Since 8836 is a perfect square, the digits of the number can be grouped into pairs: (2 x 47)^2
Step 3: Taking one number from each pair gives us the square root. Therefore, √8836 = 2 x 47 = 94.
The long division method is particularly used for finding the square root of non-perfect square numbers, but it can also confirm perfect squares. Let us learn how to find the square root using the long division method:
Step 1: Group the numbers from right to left. For 8836, group it as 88 and 36.
Step 2: Find a number whose square is less than or equal to 88. The number is 9, as 9 x 9 = 81. Subtract 81 from 88, which leaves a remainder of 7.
Step 3: Bring down 36 to make it 736. Double the quotient (9), giving us 18, and use it as our new divisor.
Step 4: Find a digit x such that (180 + x) x ≤ 736. The number is 4, as 184 x 4 = 736.
Step 5: Subtract 736 from 736 to get a remainder of 0.
Therefore, the quotient 94 is the square root of 8836.
The approximation method is not needed since 8836 is a perfect square. However, if needed, one can find perfect squares nearest to 8836.
Step 1: Recognize that 8836 is close to the perfect squares 81^2 = 6561 and 100^2 = 10000.
Step 2: Since 8836 is a perfect square, compute directly or use the prime factorization method to find the square root as 94.
Students may make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Here are a few common mistakes and how students can avoid them.
Can you help Max find the area of a square box if its side length is given as √8836?
The area of the square is 8836 square units.
The area of the square = side^2.
The side length is given as √8836.
Area of the square = side^2 = √8836 x √8836 = 94 x 94 = 8836
Therefore, the area of the square box is 8836 square units.
A square-shaped building measuring 8836 square feet is built; if each of the sides is √8836, what will be the square feet of half of the building?
4418 square feet
To find half of the area of the square-shaped building, divide the total area by 2.
Dividing 8836 by 2 = 4418
So half of the building measures 4418 square feet.
Calculate √8836 x 5.
470
First, find the square root of 8836, which is 94.
Then multiply 94 by 5.
So, 94 x 5 = 470.
What will be the square root of (8836 + 64)?
The square root is 96.
To find the square root, first calculate the sum of (8836 + 64). 8836 + 64 = 8900, and then √8900 ≈ 94.34.
Therefore, the square root of 8900 is approximately ±94.34.
Find the perimeter of the rectangle if its length ‘l’ is √8836 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 264 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√8836 + 38) = 2 × (94 + 38) = 2 × 132 = 264 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.