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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 3125.
The square root is the inverse of the square of the number. 3125 is not a perfect square. The square root of 3125 is expressed in both radical and exponential form. In the radical form, it is expressed as √3125, whereas (3125)^(1/2) in the exponential form. √3125 ≈ 55.9017, which is an irrational number because it cannot 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. However, the prime factorization method is not used for non-perfect square numbers where long division method and approximation method are used. 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 3125 is broken down into its prime factors.
Step 1: Finding the prime factors of 3125 Breaking it down, we get 5 x 5 x 5 x 5 x 5: 5^5
Step 2: Now we found out the prime factors of 3125. The second step is to make pairs of those prime factors. Since 3125 is not a perfect square, the digits of the number can’t be grouped entirely in pairs. Therefore, calculating the square root of 3125 using prime factorization involves simplifying it to √(5^2 × 5^2 × 5) = 25√5.
The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn 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 3125, we need to group it as 31 and 25.
Step 2: Now we need to find n whose square is less than or equal to 31. We can say n is '5' because 5^2 = 25 is less than 31. Now the quotient is 5, after subtracting 31-25, the remainder is 6.
Step 3: Now let us bring down 25, making the new dividend 625. Add the old divisor (5) with the same number to get 10, which will be our new divisor (5 becomes 50 when we double it as part of the calculation).
Step 4: The new divisor will be 10n; we need to find the value of n such that 10n x n ≤ 625. Choosing n as 5 works because 105 x 5 = 525.
Step 5: Subtract 525 from 625; the difference is 100, and the quotient is 55.
Step 6: Since the new dividend (100) is less than the new divisor (105), we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 10000.
Step 7: Now we need to find the new divisor, which will be 110n, where n = 9. Because 1109 ✖ 9 = 9981, which is close to 10000.
Step 8: Subtracting 9981 from 10000 gives us 19.
Step 9: Continue doing these steps until we achieve sufficient precision. So the square root of √3125 is approximately 55.9017.
The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 3125 using the approximation method.
Step 1: We need to find the closest perfect squares of √3125. The smallest perfect square below 3125 is 3025 (which is 55^2), and the largest perfect square above 3125 is 3136 (which is 56^2). √3125 falls somewhere between 55 and 56.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (3125 - 3025) / (3136 - 3025) = 100 / 111 ≈ 0.9009. Adding this value to the integer part gives us approximately 55.9009. Therefore, the square root of 3125 is approximately 55.9017.
Students do make mistakes while finding square roots, such as forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √3125?
The area of the square is 3125 square units.
The area of the square = side^2.
The side length is given as √3125.
Area of the square = side^2 = √3125 × √3125 = 3125.
Therefore, the area of the square box is 3125 square units.
A square-shaped field measuring 3125 square feet is built; if each of the sides is √3125, what will be the square feet of half of the field?
1562.5 square feet
We can divide the given area by 2 as the field is square-shaped.
Dividing 3125 by 2 = we get 1562.5.
So half of the field measures 1562.5 square feet.
Calculate √3125 × 3.
167.7051
The first step is to find the square root of 3125, which is approximately 55.9017.
The second step is to multiply 55.9017 by 3.
So 55.9017 × 3 ≈ 167.7051.
What will be the square root of (3125 + 25)?
The square root is approximately 56.7005.
To find the square root, we need to find the sum of (3125 + 25). 3125 + 25 = 3150, and then √3150 ≈ 56.7005.
Find the perimeter of the rectangle if its length 'l' is √3125 units and the width 'w' is 50 units.
The perimeter of the rectangle is approximately 211.8034 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3125 + 50) ≈ 2 × (55.9017 + 50) ≈ 2 × 105.9017 ≈ 211.8034 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.
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