145 LearnersLast updated on May 26th, 2025
Square Root of 8836
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.
What is 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.
Finding the Square Root of 8836
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:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 8836 by Prime Factorization Method
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.
Square Root of 8836 by Long Division Method
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.
Square Root of 8836 by Approximation Method
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.
Common Mistakes and How to Avoid Them in the Square Root of 8836
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.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, usually, only the positive square root is considered in practical applications.
For example: √8836 = 94, but there is also -94.
Mistake 2
Not adding the square root symbol in proper places
Misplacing the square root symbol can lead to errors. It is essential to simplify numbers inside the square root before proceeding.
For example, √(25 + 9) = √34 is incorrect; it should be √34.
Mistake 3
Not finding the correct value of a non-perfect square
Students should simplify numbers inside the square root correctly to avoid mistakes.
For example, √50 ≈ 7.071067, and not approximating properly can lead to errors.
Mistake 4
Confusing the square root symbol with the cube root
Students need to differentiate between square root and cube root symbols.
For example, √50 and ∛50 are different operations.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps, which may lead to skipped steps or incorrect subtraction, resulting in errors.
Square root of 8836 Examples
Problem 1
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.
Explanation
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.
Problem 2
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
Explanation
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.
Problem 3
Calculate √8836 x 5.
470
Explanation
First, find the square root of 8836, which is 94.
Then multiply 94 by 5.
So, 94 x 5 = 470.
Problem 4
What will be the square root of (8836 + 64)?
The square root is 96.
Explanation
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.
Problem 5
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.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√8836 + 38) = 2 × (94 + 38) = 2 × 132 = 264 units.
FAQ on Square Root of 8836
1.What is √8836 in its simplest form?
2.Mention the factors of 8836.
3.Calculate the square of 94.
4.Is 8836 a prime number?
5.8836 is divisible by?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 8836?
8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 8836?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for the Square Root of 8836
- Square root: A square root is the inverse of a square. For example, 94^2 = 8836 and the inverse of the square is the square root, so √8836 = 94.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 8836 is a perfect square because it is 94^2.
- Prime factorization: The process of expressing a number as the product of its prime factors.
- Long division method: A method used to find the square root of a number by dividing it step by step to get a quotient that is the square root.
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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.
