102 LearnersLast updated on May 26th, 2025
Square Root of 6.25
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 6.25
What is the Square Root of 6.25?
The square root is the inverse of the square of the number. 6.25 is a perfect square. The square root of 6.25 is expressed in both radical and exponential form. In the radical form, it is expressed as √6.25, whereas (6.25)^(1/2) in the exponential form. √6.25 = 2.5, 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 6.25
The prime factorization method is used for perfect square numbers. However, 6.25 is already a perfect square, so the prime factorization method is not needed. Let us explore the methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 6.25 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 6.25 is broken down into its prime factors.
Step 1: Finding the prime factors of 6.25 Since 6.25 = (2.5)^2, it is a perfect square.
The prime factorization of 6.25 is (5/2) x (5/2).
Step 2: Since 6.25 is a perfect square, we can pair the prime factors.
Therefore, the square root of 6.25 using prime factorization is 2.5.
Square Root of 6.25 by Long Division Method
The long division method is helpful for both non-perfect and perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.
Step 1: Start by grouping the digits of the number in pairs from right to left. For 6.25, we group it as 6.25.
Step 2: Find a number whose square is less than or equal to 6. The closest is 2, as 2^2 = 4.
Step 3: Subtract 4 from 6 to get the remainder 2, and bring down the next pair, 25, to make it 225.
Step 4: Double the divisor (2) to get 4, and determine the next digit of the quotient by finding a number, n, such that 4n × n ≤ 225.
Step 5: n = 5 works as 45 × 5 = 225.
Step 6: Subtract 225 from 225 to get the remainder 0.
Step 7: The quotient is 2.5, so the square root of 6.25 is 2.5.
Square Root of 6.25 by Approximation Method
The approximation method is another way for finding square roots, especially useful in estimation.
Step 1: Identify the closest perfect squares around 6.25. The perfect squares are 4 (2^2) and 9 (3^2).
Step 2: 6.25 falls between 4 and 9, so it is between 2 and 3.
Step 3: Since 6.25 is a perfect square, the square root is exactly 2.5.
Common Mistakes and How to Avoid Them in the Square Root of 6.25
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make 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 will be taking only the positive square root, as it is the required one.
For example: √6.25 = 2.5, there is also -2.5 which should not be forgotten.
Square Root of 6.25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √6.25?
The area of the square is 6.25 square units.
Explanation
The area of the square = side^2.
The side length is given as √6.25.
Area of the square = side^2 = √6.25 × √6.25 = 2.5 × 2.5 = 6.25.
Therefore, the area of the square box is 6.25 square units.
Problem 2
A square-shaped building measuring 6.25 square feet is built; if each of the sides is √6.25, what will be the square feet of half of the building?
3.125 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 6.25 by 2 = we get 3.125.
So half of the building measures 3.125 square feet.
Problem 3
Calculate √6.25 × 5.
12.5
Explanation
The first step is to find the square root of 6.25, which is 2.5.
The second step is to multiply 2.5 with 5.
So 2.5 × 5 = 12.5.
Problem 4
What will be the square root of (4 + 2.25)?
The square root is 2.5.
Explanation
To find the square root, we need to find the sum of (4 + 2.25). 4 + 2.25 = 6.25, and then √6.25 = 2.5.
Therefore, the square root of (4 + 2.25) is ±2.5.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √6.25 units and the width ‘w’ is 10 units.
We find the perimeter of the rectangle as 25 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√6.25 + 10) = 2 × (2.5 + 10) = 2 × 12.5 = 25 units.
FAQ on Square Root of 6.25
1.What is √6.25 in its simplest form?
2.Mention the factors of 6.25.
3.Calculate the square of 6.25.
4.Is 6.25 a prime number?
5.6.25 is divisible by?
Important Glossaries for the Square Root of 6.25
- Square root: A square root is the inverse of a square. Example: 2.5^2 = 6.25, and the inverse of the square is the square root, which is √6.25 = 2.5.
- 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 number that is the square of an integer. Example: 6.25 is a perfect square of 2.5.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 2.5, 3.75, and 4.5 are decimals.
- Long division method: A systematic approach used to find the square root of a number by dividing it into pairs and solving step-by-step.
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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.
