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124 LearnersLast updated on December 15, 2025
Square Root of 400/4
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 400/4.
What is the Square Root of 400/4?
The square root is the inverse of the square of the number.
400/4 simplifies to 100, which is a perfect square.
The square root of 100 is expressed in both radical and exponential form.
In the radical form, it is expressed as √100, whereas in exponential form, it is (100)^(1/2). √100 = 10, 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 400/4
For perfect square numbers, the prime factorization method is useful.
Since 100 is a perfect square, the prime factorization method, along with basic square root calculation, can be used.
Let us now learn the following methods:
- Prime factorization method
- Direct calculation
Square Root of 400/4 by Prime Factorization Method
The product of prime factors is the prime factorization of a number.
Now let us look at how 100 is broken down into its prime factors:
Step 1: Finding the prime factors of 100. Breaking it down, we get 2 x 2 x 5 x 5: 2² x 5².
Step 2: Now that we found the prime factors of 100, the second step is to make pairs of those prime factors. Since 100 is a perfect square, the digits of the number can be grouped in pairs: (2 x 5) x (2 x 5) = 10 x 10.
Step 3: Therefore, the square root of 100 using prime factorization is 10.
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Square Root of 400/4 by Direct Calculation
The direct calculation method is particularly straightforward for perfect square numbers. In this method, we calculate the square root directly:
Step 1: Simplify 400/4 to get 100.
Step 2: Recognize 100 as a perfect square, where 10 x 10 = 100.
Step 3: Therefore, the square root of 100 is 10.
Common Mistakes and How to Avoid Them in the Square Root of 400/4
Students do make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly simplifying fractions.
Now let us look at a few of those mistakes that students tend to make in detail.
Common Mistakes and How to Avoid Them in the Square Root of 400/4
Students do make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly simplifying fractions.
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 has both positive and negative square roots.
However, we usually take only the positive square root, as it is the required one.
For example: √100 = 10, but there is also -10, which should not be forgotten.
Mistake 2
Incorrectly simplifying fractions
Some students may incorrectly simplify fractions, which can lead to errors.
Ensure that the fraction is simplified before finding its square root.
For example: 400/4 should be simplified to 100 before calculating the square root.
Mistake 3
Not recognizing perfect squares
Recognizing perfect squares is crucial for quick calculations. Failing to do so can lead to unnecessary steps.
For example, not recognizing that 100 is a perfect square can lead students to use more complex methods unnecessarily.
Mistake 5
Overcomplicating simple calculations
Sometimes students overcomplicate simple calculations, such as using the long division method for perfect squares.
Emphasize recognizing when direct calculation is appropriate for simplicity.
Square Root of 400/4 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as โ(400/4)?
The area of the square is 100 square units.
Explanation
The area of the square = side².
The side length is given as √(400/4).
Area of the square = side² = √100 x √100 = 10 x 10 = 100.
Therefore, the area of the square box is 100 square units.
Problem 2
A square-shaped building measuring 400/4 square feet is built; if each of the sides is โ(400/4), what will be the square feet of half of the building?
50 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 100 by 2, we get 50.
So half of the building measures 50 square feet.
Problem 3
Calculate โ(400/4) x 5.
50
Explanation
The first step is to find the square root of 400/4, which is 10.
The second step is to multiply 10 by 5.
So, 10 x 5 = 50.
Problem 4
What will be the square root of (400/4 + 0)?
The square root is 10.
Explanation
To find the square root, we need to find the sum of (400/4 + 0).
400/4 + 0 = 100 + 0 = 100, and then √100 = ±10.
Therefore, the square root of (400/4 + 0) is ±10.
Problem 5
Find the perimeter of the rectangle if its length โlโ is โ(400/4) units and the width โwโ is 20 units.
We find the perimeter of the rectangle as 60 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√100 + 20)
= 2 × (10 + 20)
= 2 × 30
= 60 units.
FAQ on Square Root of 400/4
1.What is โ(400/4) in its simplest form?
2.What are the factors of 100?
3.Calculate the square of 100.
4.Is 100 a prime number?
5.100 is divisible by?
Important Glossaries for the Square Root of 400/4
- Square root: A square root is the inverse of a square. Example: 10² = 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 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, 100 is a perfect square because it is 10 x 10.
- Prime factorization: Prime factorization is expressing a number as the product of its prime numbers. For example, the prime factorization of 100 is 2 x 2 x 5 x 5.
- Direct calculation: Direct calculation involves finding the square root of a perfect square directly without complex methods.
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.
