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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 5904.
The square root is the inverse of the square of the number. 5904 is not a perfect square. The square root of 5904 is expressed in both radical and exponential form. In the radical form, it is expressed as √5904, whereas (5904)^(1/2) in the exponential form. √5904 ≈ 76.849, 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.
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods like 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 5904 is broken down into its prime factors:
Step 1: Finding the prime factors of 5904 Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3 x 5 x 41: 2^4 x 3^2 x 5^1 x 41^1
Step 2: Now we have found the prime factors of 5904. The second step is to make pairs of those prime factors. Since 5904 is not a perfect square, the digits of the number can’t be grouped into complete pairs.
Therefore, calculating 5904 using prime factorization as a perfect square is not possible.
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: Group the numbers from right to left. In the case of 5904, we need to group it as 04 and 59.
Step 2: Find a number whose square is less than or equal to 59. We can say this number is ‘7’ because 7 x 7 = 49, which is less than 59. Now the quotient is 7 and the remainder is 10.
Step 3: Bring down 04, making the new dividend 1004.
Step 4: Double the quotient and place it as the new divisor's first digit, i.e., 14_.
Step 5: Now find a digit to fill in the blank such that 14_ times that digit is less than or equal to 1004. The suitable digit is 7 as 147 x 7 = 1029, which is too high, so try 146 x 6 = 876.
Step 6: Subtract 876 from 1004, the remainder is 128.
Step 7: Since the remainder is less than the divisor, add a decimal point and bring down pairs of zeros.
Step 8: Continue this process to find more decimal places.
So, the square root of √5904 ≈ 76.849
The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 5904 using the approximation method.
Step 1: Find the closest perfect squares of √5904.
The smallest perfect square less than 5904 is 5776 and the largest perfect square greater than 5904 is 5929. √5904 falls somewhere between 76 and 77.
Step 2: Apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula: (5904 - 5776) ÷ (5929 - 5776) = 128 ÷ 153 = 0.8366
Using the formula, we identified the decimal point of our square root. The next step is adding the integer part, which is 76, so 76 + 0.8366 ≈ 76.84.
Therefore, the square root of 5904 is approximately 76.84.
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √5904?
The area of the square is approximately 5904 square units.
The area of the square = side².
The side length is given as √5904.
Area of the square = side² = √5904 × √5904 = 5904.
Therefore, the area of the square box is approximately 5904 square units.
A square-shaped building measuring 5904 square feet is built; if each of the sides is √5904, what will be the square feet of half of the building?
2952 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 5904 by 2 = we get 2952.
So half of the building measures 2952 square feet.
Calculate √5904 × 5.
384.245
The first step is to find the square root of 5904, which is approximately 76.849, and then multiply 76.849 by 5.
So 76.849 × 5 ≈ 384.245.
What will be the square root of (5904 + 25)?
The square root is approximately 77.
To find the square root, first find the sum of (5904 + 25) = 5929.
The square root of 5929 is exactly 77.
Therefore, the square root of (5904 + 25) is ±77.
Find the perimeter of the rectangle if its length ‘l’ is √5904 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 253.698 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√5904 + 50) ≈ 2 × (76.849 + 50) = 2 × 126.849 = 253.698 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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