Last updated on May 26th, 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.
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.
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:
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.
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.
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.
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.
Can you help Max find the area of a square box if its side length is given as √9604?
The area of the square is 9604 square units.
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.
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?
4802 square feet
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.
Calculate √9604 x 5.
490
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.
What will be the square root of (9600 + 4)?
The square root is 98.
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.
Find the perimeter of a rectangle if its length ‘l’ is √9604 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 272 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√9604 + 38) = 2 × (98 + 38) = 2 × 136 = 272 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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