128 LearnersLast updated on May 26th, 2025
Square Root of 625
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 625.
What is the Square Root of 625?
The square root is the inverse of the square of the number. 625 is a perfect square. The square root of 625 is expressed in both radical and exponential form. In the radical form, it is expressed as √625, whereas 625^(1/2) in the exponential form. √625 = 25, 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 625
The prime factorization method is used for perfect square numbers. For 625, the prime factorization method can be applied, as it is a perfect square number. Let us now learn the following methods:
- Prime factorization method
- Verification by multiplication
Square Root of 625 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 625 is broken down into its prime factors.
Step 1: Finding the prime factors of 625 Breaking it down, we get 5 x 5 x 5 x 5 = 5^4
Step 2: Now we found out the prime factors of 625. The second step is to make pairs of those prime factors. Since 625 is a perfect square, the digits can be grouped in pairs. Therefore, calculating √625 using prime factorization gives 5 x 5 = 25.
Verification by Multiplication
To verify our finding, we can multiply the square root by itself to see if we get the original number.
Step 1: Multiply 25 by itself. 25 x 25 = 625 Since we get 625, our calculation of the square root is correct.
Common Uses of Square Root of 625
The square root of 625, which is 25, is commonly used in various practical applications.
For example, knowing that 625 square feet is the area of a square, it means each side of the square is 25 feet long. This is useful in construction, land measurement, and design fields.
Common Mistakes and How to Avoid Them in the Square Root of 625
Students do make mistakes while finding the square root, like forgetting about the negative square root. 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, √625 = 25, but there is also -25 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example, √(25 + 100) ≠ √25 + √100. The right way is √(25 + 100) = √125.
Mistake 3
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them keep away from mistakes.
For example, √8 and ∛8 are different.
Mistake 4
Misidentifying perfect squares
It is crucial to correctly identify whether a number is a perfect square to apply the right method for finding its square root. Misidentifying 625 as a non-perfect square could lead to unnecessary steps in calculation.
Mistake 5
Skipping steps in prime factorization
When using prime factorization, it is important to list out all prime factors and correctly pair them to find the square root. Skipping steps or mispairing can lead to incorrect results.
Square Root of 625 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √625?
The area of the square is 625 square units.
Explanation
The area of the square = side^2.
The side length is given as √625.
Area of the square = side^2 = √625 x √625 = 25 x 25 = 625.
Therefore, the area of the square box is 625 square units.
Problem 2
A square-shaped building measuring 625 square feet is built; if each of the sides is √625, what will be the square feet of half of the building?
312.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 625 by 2 = we get 312.5
So half of the building measures 312.5 square feet.
Problem 3
Calculate √625 x 4.
100
Explanation
The first step is to find the square root of 625, which is 25.
The second step is to multiply 25 with 4. So 25 x 4 = 100.
Problem 4
What will be the square root of (400 + 225)?
The square root is 25.
Explanation
To find the square root, we need to find the sum of (400 + 225). 400 + 225 = 625, and then √625 = 25.
Therefore, the square root of (400 + 225) is ±25.
Problem 5
Find the perimeter of a square if its side is √625 units.
The perimeter of the square is 100 units.
Explanation
Perimeter of the square = 4 × side. Perimeter = 4 × √625 = 4 × 25 = 100 units.
FAQ on Square Root of 625
1.What is √625 in its simplest form?
2.Mention the factors of 625.
3.Calculate the square of 625.
4.Is 625 a prime number?
5.625 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 625?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 625?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 625
- Square root: A square root is the inverse operation of squaring a number. Example: 5^2 = 25, and the inverse is the square root: √25 = 5.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 625 is a perfect square because it is 25^2.
- Rational number: A rational number can be expressed as a fraction where both the numerator and the denominator are integers. For example, 25 is a rational number because it can be expressed as 25/1.
- Factorization: Factorization is the process of breaking down a number into a product of other numbers or factors. For example, the factorization of 625 is 5 x 5 x 5 x 5.
- Perimeter: The perimeter is the total length around a two-dimensional shape. For a square with side length s, the perimeter is 4s.
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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.
