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 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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √10000 x 5.
500
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
What will be the square root of (10000 + 0)?
The square root is 100
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.
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.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√10000 + 50) = 2 × (100 + 50) = 2 × 150 = 300 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.