Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of a square is a square root. The square root is used in various fields, including vehicle design and finance. Here, we will discuss the square root of 6250.
The square root is the inverse of squaring a number. 6250 is not a perfect square. The square root of 6250 is expressed in both radical and exponential forms. In radical form, it is expressed as √6250, whereas in exponential form, it is (6250)^(1/2). √6250 ≈ 79.05694, which is an irrational number because it cannot be expressed as a ratio of two integers.
The prime factorization method is used for perfect square numbers. For non-perfect square numbers like 6250, the 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 6250 is broken down into its prime factors:
Step 1: Finding the prime factors of 6250. Breaking it down, we get 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 2 x 5^4 x 5^2.
Step 2: Now that we have found the prime factors of 6250, the second step is to form pairs of those prime factors. Since 6250 is not a perfect square, the digits of the number can’t be grouped into complete pairs, making it challenging to calculate the exact square root using prime factorization alone.
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, we need to group the numbers from right to left. In the case of 6250, we need to group it as 50 and 62.
Step 2: Identify the largest number whose square is less than or equal to 62. We can say this number is '7' because 7 x 7 = 49, which is less than 62. Now the quotient is 7, and after subtracting 49 from 62, the remainder is 13.
Step 3: Bring down the next pair of digits, which is 50, making the new dividend 1350. Add the old divisor to itself (7 + 7 = 14) to get the new divisor.
Step 4: Find a digit 'n' such that 14n x n is less than or equal to 1350. Let us consider n as 9, then 149 x 9 = 1341.
Step 5: Subtract 1341 from 1350; the difference is 9. The quotient now becomes 79.
Step 6: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 900.
Step 7: Continue the process to find the next digit. The new divisor is 158, and since 158 x 5 = 790, the next digit in the quotient is 5.
Step 8: Subtracting 790 from 900 gives 110. Continue this process until you achieve the desired precision.
So the square root of √6250 is approximately 79.056.
The approximation method is another method for finding square roots; it is a straightforward method to estimate the square root of a given number. Now let us learn how to find the square root of 6250 using the approximation method.
Step 1: Identify the closest perfect squares to √6250.
The smallest perfect square less than 6250 is 6084, and the largest perfect square greater than 6250 is 6400. Therefore, √6250 falls between 78 and 80.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (6250 - 6084) ÷ (6400 - 6084) ≈ 0.056. Add this decimal to the smaller integer root: 78 + 0.056 = 78.056.
Therefore, the square root of 6250 is approximately 79.056.
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at some common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √6250?
The area of the square is approximately 6250 square units.
The area of a square = side^2.
The side length is given as √6250.
Area of the square = (√6250)^2 = 6250.
Therefore, the area of the square box is approximately 6250 square units.
A square-shaped plot measuring 6250 square feet is built; if each of the sides is √6250, what will be the square feet of half of the plot?
3125 square feet
To find the area of half of the plot, divide the given area by 2.
Dividing 6250 by 2 gives us 3125.
So, half of the plot measures 3125 square feet.
Calculate √6250 x 5.
395.2847
The first step is to find the square root of 6250, which is approximately 79.056.
The second step is to multiply 79.056 by 5.
So, 79.056 x 5 ≈ 395.2847.
What will be the square root of (6250 + 150)?
The square root is approximately 80.
To find the square root, first find the sum of (6250 + 150). 6250 + 150 = 6400, and √6400 = 80.
Therefore, the square root of (6250 + 150) is ±80.
Find the perimeter of the rectangle if its length ‘l’ is √6250 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 258.1139 units.
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (√6250 + 50) ≈ 2 × (79.056 + 50) ≈ 2 × 129.056 ≈ 258.1139 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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