117 LearnersLast updated on May 26th, 2025
Square Root of 40000
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 40000.
What is the Square Root of 40000?
The square root is the inverse of the square of the number. 40000 is a perfect square. The square root of 40000 is expressed in both radical and exponential form. In the radical form, it is expressed as √40000, whereas (40000)^(1/2) in the exponential form. √40000 = 200, 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 40000
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are used. Since 40000 is a perfect square, we will primarily use the prime factorization method. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 40000 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 40000 is broken down into its prime factors.
Step 1: Finding the prime factors of 40000 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 40000. The second step is to make pairs of those prime factors. Since 40000 is a perfect square, the digits of the number can be grouped in pairs.
Therefore, calculating √40000 using prime factorization gives us: (2^4) x (5^4) = (2 x 5)^2 = 200.
Square Root of 40000 by Long Division Method
The long division method is particularly used for non-perfect square numbers, but it can also be applied to perfect squares. Here’s 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 40000, we group it as (400)(00).
Step 2: Now we need to find n whose square is less than or equal to 400. We can say n as '20' because 20 x 20 = 400.
Step 3: The quotient is 20 after subtracting 400 - 400, the remainder is 0.
Since the remainder is 0, the square root of 40000 is 200.
Square Root of 40000 by Approximation Method
The approximation method is another way to find square roots. It is an easy method for estimating the square root of a given number, especially when it is not a perfect square. However, for 40000, we know the exact value, which is 200. Therefore, this method is unnecessary here.
Common Mistakes and How to Avoid Them in the Square Root of 40000
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods like long division. Now let us look at a few of those mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we usually take only the positive square root, as it is the required one.
For example: √40000 = 200, but there is also -200, which should not be forgotten.
Square Root of 40000 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √40000?
The area of the square is 40000 square units.
Explanation
The area of the square = side^2.
The side length is given as √40000.
Area of the square = side^2 = √40000 x √40000 = 200 × 200 = 40000
Therefore, the area of the square box is 40000 square units.
Problem 2
A square-shaped building measuring 40000 square feet is built; if each of the sides is √40000, what will be the square feet of half of the building?
20000 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 40000 by 2 = we get 20000 So half of the building measures 20000 square feet.
Problem 3
Calculate √40000 x 5.
1000
Explanation
The first step is to find the square root of 40000, which is 200, and the second step is to multiply 200 by 5.
So 200 x 5 = 1000.
Problem 4
What will be the square root of (39500 + 500)?
The square root is 200.
Explanation
To find the square root, we need to find the sum of (39500 + 500).
39500 + 500 = 40000, and then √40000 = 200.
Therefore, the square root of (39500 + 500) is ±200.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √40000 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as 500 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√40000 + 50) = 2 × (200 + 50) = 2 × 250 = 500 units.
FAQ on Square Root of 40000
1.What is √40000 in its simplest form?
2.Mention the factors of 40000.
3.Calculate the square of 40000.
4.Is 40000 a prime number?
5.40000 is divisible by?
Important Glossaries for the Square Root of 40000
- Square root: A square root is the inverse of a square. For example: 20^2 = 400, and the inverse of the square is the square root, which is √400 = 20.
- 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 a number that is the square of an integer. For example, 40000 is a perfect square because it is the square of 200.
- Integer: Integers are the combination of whole numbers and their negatives. For example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, etc., are integers.
- Prime factorization: Prime factorization involves breaking down a number into its prime factors. For example, the prime factorization of 40000 is 2^4 × 5^4.
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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.
