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 3593.
The square root is the inverse of the square of the number. 3593 is not a perfect square. The square root of 3593 is expressed in both radical and exponential forms. In the radical form, it is expressed as √3593, whereas (3593)^(1/2) in the exponential form. √3593 ≈ 59.931, 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 typically used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where 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 3593 is broken down into its prime factors.
Step 1: Finding the prime factors of 3593 3593 is a prime number, so it itself is its prime factor.
Step 2: Since 3593 is not a perfect square, calculating its square root using prime factorization is not feasible.
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: To begin with, we need to group the numbers from right to left. In the case of 3593, we need to group it as 93 and 35.
Step 2: Now, we need to find n whose square is less than or equal to 35. We can say n as '5' because 5 × 5 = 25 is less than 35. Now the quotient is 5, and after subtracting 25 from 35, the remainder is 10.
Step 3: Now let us bring down 93, which is the new dividend. Add the old divisor with the same number 5 + 5 to get 10, which will be our new divisor.
Step 4: We need to find n such that 10n × n ≤ 1093; let us consider n as 9, now 109 × 9 = 981.
Step 5: Subtract 981 from 1093, the difference is 112, and the quotient is 59.
Step 6: Since the dividend is less than the divisor, we add a decimal point to the quotient and add two zeroes to the dividend. The new dividend is 11200.
Step 7: Find the new divisor that is 598, because 598 × 1 = 598.
Step 8: Subtracting 598 from 11200 gives us the remainder 10602.
Step 9: Continue this process until the desired precision is achieved.
The square root of 3593 is approximately 59.931.
The approximation method is another method for finding square roots. It is an easy way to find the square root of a given number. Now let us learn how to find the square root of 3593 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √3593. The smallest perfect square less than 3593 is 3481 (59²) and the largest perfect square greater than 3593 is 3600 (60²). Thus, √3593 falls between 59 and 60.
Step 2: Apply the formula: (Given number - smallest perfect square) / (next perfect square - smallest perfect square) (3593 - 3481) / (3600 - 3481) = 112 / 119 ≈ 0.941 Adding this to 59 gives us 59 + 0.941 ≈ 59.941.
So the square root of 3593 is approximately 59.941.
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max find the area of a square box if its side length is given as √3593?
The area of the square is approximately 3593 square units.
The area of the square = side².
The side length is given as √3593.
Area of the square = side² = √3593 × √3593 = 3593.
Therefore, the area of the square box is 3593 square units.
A square-shaped building measuring 3593 square feet is built; if each of the sides is √3593, what will be the square feet of half of the building?
1796.5 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3593 by 2 = 1796.5.
So half of the building measures 1796.5 square feet.
Calculate √3593 × 5.
Approximately 299.655
The first step is to find the square root of 3593, which is approximately 59.931.
The second step is to multiply 59.931 with 5.
So 59.931 × 5 ≈ 299.655.
What will be the square root of (3593 + 7)?
The square root is approximately 60.
To find the square root, we need to find the sum of (3593 + 7).
3593 + 7 = 3600, and then √3600 = 60.
Therefore, the square root of (3593 + 7) is ±60.
Find the perimeter of the rectangle if its length ‘l’ is √3593 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 195.862 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3593 + 38)
= 2 × (59.931 + 38)
= 2 × 97.931
≈ 195.862 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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