Square Root of 2401
2026-02-28 09:46 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 the square is a square root. The square root is used in fields such as vehicle design and finance. Here, we will discuss the square root of 2401.

What is the Square Root of 2401?

The square root is the inverse of the square of a number. 2401 is a perfect square. The square root of 2401 is expressed in both radical and exponential form. In radical form, it is expressed as √2401, whereas in exponential form it is expressed as (2401)^(1/2). √2401 = 49, 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.

Finding the Square Root of 2401

The prime factorization method is used for perfect square numbers. Since 2401 is a perfect square, we can use its prime factorization to find the square root. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 2401 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 2401 is broken down into its prime factors:

Step 1: Finding the prime factors of 2401 Breaking it down, we get 7 x 7 x 7 x 7; that is, 7^4.

Step 2: Now we found out the prime factors of 2401. Since 2401 is a perfect square, the square root is the product of one number from each pair of the same factors.

Therefore, √2401 = 7 * 7 = 49.

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Square Root of 2401 by Long Division Method

The long division method can also be used for perfect squares to verify the result. Let us now learn how to find the square root using the long division method, step by step.

Step 1: Group the numbers from right to left. In the case of 2401, group it as 24 and 01.

Step 2: Find the largest number whose square is less than or equal to 24. Here, it is 4, as 4^2 = 16. Subtract 16 from 24 to get a remainder of 8.

Step 3: Bring down the next pair of digits, 01, to make the new dividend 801.

Step 4: Double the divisor (4) to get 8, and use it to find the next digit of the quotient. Find a digit x such that 8x * x is less than or equal to 801. Here, x is 9, as 89 * 9 = 801.

Step 5: Therefore, the quotient is 49, which is the square root of 2401.

Square Root of 2401 by Approximation Method

The approximation method is generally used for finding the square roots of non-perfect squares. However, since 2401 is a perfect square, the exact root can be found without approximation. For completeness, we check the perfect squares near 2401:

Step 1: The perfect squares closest to 2401 are 2304 (48^2) and 2500 (50^2). Since 2401 is a perfect square, its root is exactly 49, as it lies directly between these two numbers.

Step 2: No further approximation is necessary, as 2401 is a perfect square.

Common Mistakes and How to Avoid Them in the Square Root of 2401

Students may make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods. Now let us look at a few of those mistakes that students tend to make 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 √2401?

Okay, lets begin

The area of the square is 2401 square units.

Explanation

The area of the square = side^2.

The side length is given as √2401.

Area of the square = side^2 = √2401 x √2401 = 49 × 49 = 2401.

Therefore, the area of the square box is 2401 square units.

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Problem 2

A square-shaped building measuring 2401 square feet is built; if each of the sides is √2401, what will be the square feet of half of the building?

Okay, lets begin

1200.5 square feet

Explanation

We can divide the given area by 2 as the building is square-shaped.

Dividing 2401 by 2 = we get 1200.5.

So half of the building measures 1200.5 square feet.

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Problem 3

Calculate √2401 x 5.

Okay, lets begin

245

Explanation

The first step is to find the square root of 2401, which is 49.

The second step is to multiply 49 by 5.

So 49 x 5 = 245.

Well explained 👍

Problem 4

What will be the square root of (2400 + 1)?

Okay, lets begin

The square root is 49.

Explanation

To find the square root, we need to find the sum of (2400 + 1).

2400 + 1 = 2401, and then √2401 = 49.

Therefore, the square root of (2400 + 1) is ±49.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √2401 units and the width ‘w’ is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as 174 units.

Explanation

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

Perimeter = 2 × (√2401 + 38) = 2 × (49 + 38) = 2 × 87 = 174 units.

Well explained 👍

FAQ on Square Root of 2401

1.What is √2401 in its simplest form?

The prime factorization of 2401 is 7 x 7 x 7 x 7, so the simplest form of √2401 = √(7 x 7 x 7 x 7) = 49.

2.Mention the factors of 2401.

Factors of 2401 are 1, 7, 49, 343, and 2401.

3.Calculate the square of 49.

We get the square of 49 by multiplying the number by itself, that is 49 x 49 = 2401.

4.Is 2401 a prime number?

2401 is not a prime number, as it has more than two factors.

5.2401 is divisible by?

2401 is divisible by 1, 7, 49, 343, and 2401.

Important Glossaries for the Square Root of 2401

  • Square root: A square root is the inverse operation of squaring a number. For example, if 49^2 = 2401, then the square root of 2401 is 49.
  • Rational number: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where the denominator q is not zero.
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 49 is a perfect square because it is 7^2.
  • Prime factorization: Prime factorization is expressing a number as the product of its prime numbers. For instance, 2401 = 7^4.
  • Long division method: A method used to find the square root of numbers by dividing and finding approximations step by step.

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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.