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 1313.
The square root is the inverse of the square of the number. 1313 is not a perfect square. The square root of 1313 is expressed in both radical and exponential form. In the radical form, it is expressed as √1313, whereas (1313)^(1/2) in the exponential form. √1313 ≈ 36.2361, 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 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 1313 is broken down into its prime factors.
Step 1: Finding the prime factors of 1313 1313 can be broken down into 13 × 101
Step 2: Now we found out the prime factors of 1313. The second step is to make pairs of those prime factors. Since 1313 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 1313 using prime factorization is impossible.
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 1313, we need to group it as 13 and 13.
Step 2: Now we need to find n whose square is less than or equal to the leftmost group which is 13. We can say n as ‘3’ because 3 × 3 = 9, which is less than 13. Now, the quotient is 3 after subtracting 9 from 13, and the remainder is 4.
Step 3: Now let us bring down the next pair which is 13, making the new dividend 413. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.
Step 4: We need to find a digit x such that 6x × x ≤ 413. Let x be 6, then 66 × 6 = 396.
Step 5: Subtract 396 from 413, the difference is 17, and the quotient is 36.
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 1700.
Step 7: We need to find the new digit x such that 726x × x ≤ 1700. Let x be 2, then 722 × 2 = 1444.
Step 8: Subtracting 1444 from 1700 gives us the result 256. The quotient is now 36.2.
Step 9: Continue doing these steps until we get sufficient decimal places. For instance, continue until the remainder is zero or you have an accurate value.
So the square root of √1313 ≈ 36.2361.
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 1313 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √1313. The smallest perfect square less than 1313 is 1296 and the largest perfect square greater than 1313 is 1344. √1313 falls somewhere between 36 and 37.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1313 - 1296) / (1344 - 1296) ≈ 0.36. 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 36 + 0.2361 = 36.2361, so the square root of 1313 is approximately 36.2361.
Students do make mistakes while finding the square root, like forgetting about the negative square root and skipping long division methods, etc. 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 √1500?
The area of the square is 1500 square units.
The area of the square = side².
The side length is given as √1500.
Area of the square = side² = √1500 × √1500 = 1500.
Therefore, the area of the square box is 1500 square units.
A square-shaped garden measuring 1313 square feet is built; if each of the sides is √1313, what will be the square feet of half of the garden?
656.5 square feet
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 1313 by 2 = we get 656.5.
So half of the garden measures 656.5 square feet.
Calculate √1313 × 4.
144.9444
The first step is to find the square root of 1313 which is approximately 36.2361.
The second step is to multiply 36.2361 by 4.
So 36.2361 × 4 ≈ 144.9444.
What will be the square root of (1300 + 13)?
The square root is approximately 36.2361.
To find the square root, we need to find the sum of (1300 + 13).
1300 + 13 = 1313, and then √1313 ≈ 36.2361.
Therefore, the square root of (1300 + 13) is approximately ±36.2361.
Find the perimeter of the rectangle if its length ‘l’ is √1300 units and the width ‘w’ is 13 units.
We find the perimeter of the rectangle as 112.385 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1300 + 13) ≈ 2 × (36.0555 + 13) = 2 × 49.0555 ≈ 98.111 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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