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 the field of vehicle design, finance, etc. Here, we will discuss 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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √625 x 4.
100
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.
What will be the square root of (400 + 225)?
The square root is 25.
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.
Find the perimeter of a square if its side is √625 units.
The perimeter of the square is 100 units.
Perimeter of the square = 4 × side. Perimeter = 4 × √625 = 4 × 25 = 100 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.