Square Root of 9604
2026-02-28 09:12 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 9604.

What is the Square Root of 9604?

The square root is the inverse of the square of the number. 9604 is a perfect square. The square root of 9604 is expressed in both radical and exponential form. In the radical form, it is expressed as √9604, whereas (9604)^(1/2) in the exponential form. √9604 = 98, 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 9604

The prime factorization method can be used for perfect square numbers. 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 9604 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 9604 is broken down into its prime factors.

Step 1: Finding the prime factors of 9604

Breaking it down, we get 2 x 2 x 7 x 7 x 7 x 7: 2^2 x 7^4

Step 2: Now we have found the prime factors of 9604. The second step is to make pairs of those prime factors. Since 9604 is a perfect square, the digits of the number can be grouped in pairs. Therefore, the square root of 9604 using prime factorization is 2 x 7 x 7 = 98.

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Square Root of 9604 by Long Division Method

The long division method is particularly useful for finding the square root of numbers, especially when they are not perfect squares. However, let's see how it works for 9604:

Step 1: To begin with, we need to group the numbers from right to left. In the case of 9604, we group it as 96 and 04.

Step 2: Now, find the largest number whose square is less than or equal to 96. We can say that number is 9 because 9 x 9 = 81, which is less than 96. The quotient is 9 and the remainder is 96 - 81 = 15.

Step 3: Bring down the next pair, 04, making the new dividend 1504. Add 9 to itself to get 18 as the new divisor's first part.

Step 4: Guess the largest possible digit to fill the blank in 18_ (let's call it n) such that 18n x n is less than or equal to 1504. After calculating, n comes out to be 8.

Step 5: 188 x 8 = 1504, subtracting 1504 from 1504 gives a remainder of 0.

Thus, the quotient is 98, and the square root of 9604 is 98.

Square Root of 9604 by Approximation Method

The approximation method can be used to estimate the square roots, but it is more suited for non-perfect squares. For perfect squares like 9604, the exact square root can be found as shown in the previous methods. However, let's see an example of estimation:

Step 1: Identify the closest perfect squares around 9604. We know that 9801 (99^2) and 9604 (98^2) are perfect squares.

Step 2: Since 9604 is exactly 98^2, we don't need further approximation.

The square root of 9604 is precisely 98.

Common Mistakes and How to Avoid Them in the Square Root of 9604

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 a few of these 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 √9604?

Okay, lets begin

The area of the square is 9604 square units.

Explanation

The area of the square = side^2.

The side length is given as √9604.

Area of the square = side^2 = √9604 x √9604 = 98 x 98 = 9604.

Therefore, the area of the square box is 9604 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 9604 square feet is built; if each of the sides is √9604, what will be the square feet of half of the building?

Okay, lets begin

4802 square feet

Explanation

Divide the given area by 2 as the building is square-shaped.

Dividing 9604 by 2 = 4802.

So half of the building measures 4802 square feet.

Well explained 👍

Problem 3

Calculate √9604 x 5.

Okay, lets begin

490

Explanation

The first step is to find the square root of 9604, which is 98.

The second step is to multiply 98 by 5.

So 98 x 5 = 490.

Well explained 👍

Problem 4

What will be the square root of (9600 + 4)?

Okay, lets begin

The square root is 98.

Explanation

To find the square root, sum (9600 + 4) = 9604.

The square root of 9604 is 98.

Therefore, the square root of (9600 + 4) is ±98.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √9604 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is 272 units.

Explanation

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

Perimeter = 2 × (√9604 + 38) = 2 × (98 + 38) = 2 × 136 = 272 units.

Well explained 👍

FAQ on Square Root of 9604

1.What is √9604 in its simplest form?

The prime factorization of 9604 is 2^2 x 7^4, so the simplest form of √9604 = √(2^2 x 7^4) = 98.

2.Mention the factors of 9604.

The factors of 9604 include 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, and 9604.

3.Calculate the square of 98.

We get the square of 98 by multiplying the number by itself, that is 98 x 98 = 9604.

4.Is 9604 a prime number?

9604 is not a prime number, as it has more than two factors.

5.9604 is divisible by?

9604 has several factors; it is divisible by 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, and 9604.

Important Glossaries for the Square Root of 9604

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.
     
  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.
     
  • Principal square root: A number has both positive and negative square roots. However, the positive square root is often used in real-world applications and is known as the principal square root
    .
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 9604 is a perfect square because it is 98^2.
     
  • Factorization: The process of breaking down a number into its prime factors. For example, the factorization of 9604 is 2^2 x 7^4.

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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.