Square Root of 4250
2026-02-28 08:06 Diff
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Last updated on August 5, 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 various fields such as engineering, physics, and finance. Here, we will discuss the square root of 4250.

What is the Square Root of 4250?

The square root is the inverse of the square of the number. 4250 is not a perfect square. The square root of 4250 is expressed in both radical and exponential form. In the radical form, it is expressed as √4250, whereas (4250)^(1/2) in the exponential form. √4250 ≈ 65.192, 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.

Finding the Square Root of 4250

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are used. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 4250 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 4250 is broken down into its prime factors.

Step 1: Finding the prime factors of 4250 Breaking it down, we get 2 x 5 x 5 x 17 x 5: 2^1 x 5^3 x 17^1

Step 2: Now we found out the prime factors of 4250. The next step is to make pairs of those prime factors. Since 4250 is not a perfect square, the digits of the number can’t be grouped into pairs.

Therefore, calculating 4250 using prime factorization is not straightforward.

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Square Root of 4250 by Long Division Method

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: Begin by grouping the digits from right to left. For 4250, we group it as 50 and 42.

Step 2: Find n whose square is ≤ 42. We can say n is 6 because 6 x 6 = 36 which is less than or equal to 42. Now, the quotient is 6. After subtracting 36 from 42, the remainder is 6.

Step 3: Bring down the next pair of digits, 50, to make the new dividend 650. Add the old divisor with the same number, 6 + 6 = 12, which will be our new divisor.

Step 4: Determine the next digit for the quotient. Consider 12n as the new divisor. We need to find n such that 12n x n ≤ 650. Let n be 5, now 125 x 5 = 625.

Step 5: Subtract 625 from 650; the difference is 25. Since the remainder is less than the divisor, we add a decimal point to the quotient and bring down two zeros, making the new dividend 2500.

Step 6: Consider the new divisor as 130 (after adding the previous quotient digit 5 to 125) and find n such that 130n x n ≤ 2500. Let n be 1, now 130 x 1 = 130.

Step 7: Subtract 130 from 2500 to get 2370. Continue this process to determine more decimal places.

So, the square root of √4250 is approximately 65.192.

Square Root of 4250 by Approximation Method

The approximation method is another way to find square roots; it is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 4250 using the approximation method.

Step 1: Find the closest perfect squares around 4250. The closest perfect square below 4250 is 4225 (65^2), and the closest perfect square above 4250 is 4356 (66^2). Therefore, √4250 falls between 65 and 66.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (4250 - 4225) / (4356 - 4225) ≈ 0.192 Using the formula, we identified the decimal value of our square root approximation. Add this value to the integer part: 65 + 0.192 = 65.192, so the square root of 4250 is approximately 65.192.

Common Mistakes and How to Avoid Them in the Square Root of 4250

Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let's look at a few common mistakes in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √4250?

Okay, lets begin

The area of the square is approximately 4250 square units.

Explanation

The area of a square = side^2.

The side length is given as √4250.

Area of the square = side^2 = √4250 x √4250 = 4250.

Therefore, the area of the square box is approximately 4250 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 4250 square feet is built; if each of the sides is √4250, what will be the square feet of half of the building?

Okay, lets begin

2125 square feet

Explanation

For a square-shaped building, dividing the area by 2 gives the area of half the building.

Dividing 4250 by 2 = 2125.

So half of the building measures 2125 square feet.

Well explained 👍

Problem 3

Calculate √4250 x 5.

Okay, lets begin

Approximately 325.96

Explanation

The first step is to find the square root of 4250, which is approximately 65.192.

Then, multiply 65.192 by 5.

So 65.192 x 5 ≈ 325.96.

Well explained 👍

Problem 4

What will be the square root of (4250 + 100)?

Okay, lets begin

The square root is approximately 66.

Explanation

To find the square root, first calculate the sum of (4250 + 100).

4250 + 100 = 4350, and then √4350 ≈ 66.

Therefore, the square root of (4250 + 100) is approximately ±66.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √4250 units and the width ‘w’ is 50 units.

Okay, lets begin

The perimeter of the rectangle is approximately 230.384 units.

Explanation

Perimeter of a rectangle = 2 × (length + width).

Perimeter = 2 × (√4250 + 50)

= 2 × (65.192 + 50)

= 2 × 115.192

= 230.384 units.

Well explained 👍

FAQ on Square Root of 4250

1.What is √4250 in its simplest form?

The prime factorization of 4250 is 2 x 5 x 5 x 17 x 5, so the simplest form of √4250 is √(2 x 5^3 x 17).

2.Mention the factors of 4250.

Factors of 4250 are 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850, 2125, and 4250.

3.Calculate the square of 4250.

We get the square of 4250 by multiplying the number by itself, that is 4250 x 4250 = 18,062,500.

4.Is 4250 a prime number?

4250 is not a prime number, as it has more than two factors.

5.4250 is divisible by?

4250 has several factors, including 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850, 2125, and 4250.

Important Glossaries for the Square Root of 4250

  • Square root: A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse is √16 = 4.
     
  • Irrational number: An irrational number is a number that cannot be expressed as a fraction p/q, where q is not zero and p and q are integers. Example: √2.
     
  • Principal square root: A number has both positive and negative square roots; however, the positive square root is typically used in real-world applications, known as the principal square root.
     
  • Prime factorization: The expression of a number as a product of prime numbers. Example: The prime factorization of 18 is 2 x 3 x 3.
     
  • Decimal approximation: A method to estimate an irrational square root to a certain number of decimal places. Example: √2 ≈ 1.414.

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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.

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