131 LearnersLast updated on May 26th, 2025
Square Root of 10000
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 10000.
What is the Square Root of 10000?
The square root is the inverse of the square of the number. 10000 is a perfect square. The square root of 10000 is expressed in both radical and exponential form. In the radical form, it is expressed as √10000, whereas (10000)^(1/2) in the exponential form. √10000 = 100, 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 10000
The prime factorization method is used for perfect square numbers. For perfect square numbers like 10000, both the prime factorization method and direct calculation can be used. Let us now learn the following methods:
- Prime factorization method
- Direct calculation method
Square Root of 10000 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 10000 is broken down into its prime factors.
Step 1: Finding the prime factors of 10000
Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5: 2^4 x 5^4
Step 2: Now we found out the prime factors of 10000. The second step is to make pairs of those prime factors. Since 10000 is a perfect square, the digits can be grouped in pairs. Therefore, the square root of 10000 is 2^2 x 5^2 = 100.
Square Root of 10000 by Direct Calculation Method
For perfect squares, the direct calculation method is simple and efficient. Let us now learn how to find the square root using this method, step by step.
Step 1: Identify that 10000 is a perfect square.
Step 2: Recognize that 100^2 = 10000, therefore √10000 = 100.
Square Root of 10000 by Approximation Method
The approximation method is not necessary for perfect squares, but for completeness, let's discuss it briefly.
Step 1: Estimate the closest perfect squares around 10000. In this case, 10000 itself is a perfect square.
Step 2: Since 100^2 = 10000, the square root is exactly 100, making approximation unnecessary in this case.
Common Mistakes and How to Avoid Them in the Square Root of 10000
Students might make mistakes while finding the square root, such as forgetting about the negative square root or confusing it with other operations. Here are a few common mistakes to avoid.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number does have both positive and negative square roots. However, typically we consider only the positive square root for practical purposes.
For example: √10000 = 100, there is also -100 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 can occur. Remember to simplify numbers inside the square root before moving forward.
For example: √(2500 + 2500) = √5000 is not equal to √2500 + √2500.
Mistake 3
Confusing squares and square roots
Ensure students differentiate between squaring a number and finding its square root. For example, 100^2 is not the same as √10000.
Mistake 4
Confusing the square root symbol with the cube root
Students should clearly understand the difference between cube roots and square roots.
For example, √10000 and ∛10000 are different.
Mistake 5
Mistaking a non-perfect square for a perfect square
Ensure students verify whether a number is a perfect square before applying specific methods.
For example, recognizing that 10000 is a perfect square simplifies the process.
Square Root of 10000 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √10000?
The area of the square is 10000 square units.
Explanation
The area of the square = side^2.
The side length is given as √10000.
Area of the square = side^2 = √10000 x √10000 = 100 x 100 = 10000.
Therefore, the area of the square box is 10000 square units.
Problem 2
A square-shaped building measuring 10000 square feet is built; if each of the sides is √10000, what will be the square feet of half of the building?
5000 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 10000 by 2 = 5000
So half of the building measures 5000 square feet.
Problem 3
Calculate √10000 x 5.
500
Explanation
The first step is to find the square root of 10000, which is 100.
The second step is to multiply 100 by 5.
So 100 x 5 = 500
Problem 4
What will be the square root of (10000 + 0)?
The square root is 100
Explanation
To find the square root, we need to sum (10000 + 0), which is 10000.
Since 10000 is a perfect square, √10000 = 100.
Therefore, the square root of (10000 + 0) is ±100.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √10000 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is 300 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√10000 + 50) = 2 × (100 + 50) = 2 × 150 = 300 units.
FAQ on Square Root of 10000
1.What is √10000 in its simplest form?
2.Mention the factors of 10000.
3.Calculate the square of 100.
4.Is 10000 a prime number?
5.10000 is divisible by?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of 10000?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of 10000?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for the Square Root of 10000
- Square root: A square root is the inverse of a square. Example: 10^2 = 100, and the inverse of the square is the square root, that is √100 = 10.
- Rational number: A rational number is a number that can be expressed 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 a number that is the square of an integer. For example, 10000 is a perfect square because it is 100^2.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors. Example: 10000 = 2^4 x 5^4.
- Integer: Integers are whole numbers that can be positive, negative, or zero. Examples include -3, 0, 1, 2, 3, etc.
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About BrightChamps in United Arab Emirates
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.
