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 793.
The square root is the inverse of the square of the number. 793 is not a perfect square. The square root of 793 is expressed in both radical and exponential form. In the radical form, it is expressed as √793, whereas (793)^(1/2) in the exponential form. √793 ≈ 28.14, 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, 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 793 is broken down into its prime factors.
Step 1: Finding the prime factors of 793 Breaking it down, we get 13 x 61: 13^1 x 61^1.
Step 2: Now we found out the prime factors of 793. The second step is to make pairs of those prime factors. Since 793 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating 793 using prime factorization to find its square root is not straightforward.
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 793, we need to group it as 93 and 7.
Step 2: Now we need to find n whose square is less than or equal to 7. We can say n as ‘2’ because 2 x 2 = 4 is lesser than or equal to 7. Now the quotient is 2 and after subtracting 4 from 7, the remainder is 3.
Step 3: Now let us bring down 93, making the new dividend 393. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 393. Let n be 7, then 47 x 7 = 329.
Step 5: Subtract 329 from 393, the difference is 64, and the quotient is 27.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 6400.
Step 7: Now we need to find the new divisor which is 541 because 541 x 1 = 541.
Step 8: Subtracting 541 from 6400 gives the result 5859.
Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.
So the square root of √793 is approximately 28.14.
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 793 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √793.
The smallest perfect square less than 793 is 784 and the largest perfect square greater than 793 is 841. √793 falls somewhere between 28 and 29.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square) Going by the formula: (793 - 784) ÷ (841 - 784) ≈ 0.158
Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 28 + 0.158 ≈ 28.158, so the square root of 793 is approximately 28.158.
Students do make mistakes while finding the square root, such as 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 √793?
The area of the square is approximately 793 square units.
The area of the square = side^2.
The side length is given as √793.
Area of the square = side^2 = √793 x √793 = 793.
Therefore, the area of the square box is approximately 793 square units.
A square-shaped building measuring 793 square feet is built; if each of the sides is √793, what will be the square feet of half of the building?
396.5 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 793 by 2 gives us 396.5.
So half of the building measures 396.5 square feet.
Calculate √793 x 5.
140.7
The first step is to find the square root of 793, which is approximately 28.14.
The second step is to multiply 28.14 by 5.
So 28.14 x 5 ≈ 140.7.
What will be the square root of (793 + 7)?
The square root is 28.
To find the square root, we need to find the sum of (793 + 7). 793 + 7 = 800, and then √800 ≈ 28.284.
Therefore, the approximate square root of (793 + 7) is ±28.284.
Find the perimeter of the rectangle if its length ‘l’ is √793 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 132.28 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√793 + 38) ≈ 2 × (28.14 + 38) ≈ 2 × 66.14 ≈ 132.28 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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