Square Root of 7025
2026-02-28 17:53 Diff
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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in various fields like engineering, finance, etc. Here, we will discuss the square root of 7025.

What is the Square Root of 7025?

The square root is the inverse operation of squaring a number. Since 7025 is not a perfect square, its square root is expressed in both radical and exponential forms. In radical form, it is expressed as √7025, whereas in exponential form, it is (7025)^(1/2). The approximate value of √7025 is 83.8109, which is an irrational number because it cannot be exactly expressed as a fraction p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 7025

For perfect square numbers, the prime factorization method is useful. However, for non-perfect square numbers like 7025, methods such as the long division and approximation methods are used. Let us learn these methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 7025 by Prime Factorization Method

The product of prime factors is known as the prime factorization of a number. Let's examine how 7025 is decomposed into its prime factors:

Step 1: Identify the prime factors of 7025. Breaking it down, we get 5 x 5 x 281: 5^2 x 281^1

Step 2: Now that we have identified the prime factors of 7025, the next step is to pair those prime factors. Since 7025 is not a perfect square, the digits cannot be grouped into perfect pairs, making it impossible to calculate √7025 using prime factorization alone.

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Square Root of 7025 by Long Division Method

The long division method is particularly used for non-perfect squares. In this method, we find the closest perfect square number to the given number. Let us learn how to find the square root using the long division method, step by step:

Step 1: Group the numbers from right to left. For 7025, group as 25 and 70.

Step 2: Find a number whose square is less than or equal to 70. This number is 8 because 8^2 = 64. The quotient is 8 and the remainder is 70 - 64 = 6.

Step 3: Bring down 25, making the new dividend 625. Add 8 (the previous divisor) to itself to get 16, which is our new divisor base.

Step 4: Find a digit n such that 16n × n ≤ 625. Let n be 3, then 163 × 3 = 489.

Step 5: Subtract 489 from 625, giving a remainder of 136.

Step 6: Add decimal point and zeros to continue the division. The quotient so far is 83, and the process can continue to find more decimal places.

Step 7: Continue these steps until the required precision is achieved. So the square root of 7025 is approximately 83.8109.

Square Root of 7025 by Approximation Method

The approximation method is another technique for finding square roots, providing an easy way to find the square root of a given number. Let's find the square root of 7025 using this method.

Step 1: Identify the closest perfect squares to 7025. The smallest perfect square is 6889 (83^2) and the largest is 7056 (84^2). √7025 falls between 83 and 84.

Step 2: Apply the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Using the formula: (7025 - 6889) / (7056 - 6889) = 0.8109 Thus, the square root of 7025 is approximately 83 + 0.8109 = 83.8109.

Common Mistakes and How to Avoid Them in the Square Root of 7025

Students often make mistakes while finding square roots, such as forgetting about both positive and negative square roots, skipping steps in the long division method, etc. Let's look at some 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 √7025?

Okay, lets begin

The area of the square is approximately 7025 square units.

Explanation

The area of the square = side^2. The side length is given as √7025. Area of the square = (√7025)^2 = 7025. Therefore, the area of the square box is approximately 7025 square units.

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Problem 2

A square-shaped garden measures 7025 square feet in area. If each side is √7025 feet long, what will be the area of half of the garden?

Okay, lets begin

3512.5 square feet

Explanation

Since the garden is square-shaped, half of the garden's area is half of the total area. Dividing 7025 by 2 = 3512.5 square feet.

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Problem 3

Calculate √7025 × 5.

Okay, lets begin

Approx. 419.0545

Explanation

First, find the square root of 7025, which is approximately 83.8109. Then multiply 83.8109 by 5. So, 83.8109 × 5 ≈ 419.0545.

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Problem 4

What will be the square root of (7025 + 9)?

Okay, lets begin

Approx. 84.

Explanation

To find the square root, add 7025 and 9 to get 7034. The square root of 7034 is approximately 84.

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Problem 5

Find the perimeter of a rectangle if its length 'l' is √7025 units and the width 'w' is 30 units.

Okay, lets begin

Approx. 227.6218 units.

Explanation

Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√7025 + 30) = 2 × (83.8109 + 30) ≈ 2 × 113.8109 ≈ 227.6218 units.

Well explained 👍

FAQ on Square Root of 7025

1.What is √7025 in its simplest form?

The prime factorization of 7025 is 5 × 5 × 281, so the simplest form of √7025 = √(5^2 × 281).

2.Mention the factors of 7025.

Factors of 7025 include 1, 5, 25, 281, 1405, and 7025.

3.Calculate the square of 7025.

The square of 7025 is 7025 × 7025 = 49,350,625.

4.Is 7025 a prime number?

7025 is not a prime number, as it has more than two factors.

5.7025 is divisible by?

7025 is divisible by 1, 5, 25, 281, 1405, and 7025.

Important Glossaries for the Square Root of 7025

  • Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16.
     
  • Irrational number: An irrational number cannot be expressed as a simple fraction. It has an infinite and non-repeating decimal expansion.
     
  • Principal square root: The principal square root is the non-negative square root of a number.
     
  • Decimal: A number that contains a decimal point, representing a whole number and fractional part.
     
  • Prime factorization: Breaking down a number into its basic building blocks, which are prime numbers. For example, the prime factorization of 7025 is 5 × 5 × 281.

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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.