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 such as vehicle design, finance, etc. Here, we will discuss the square root of 1301.
The square root is the inverse of the square of the number. 1301 is not a perfect square. The square root of 1301 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1301, whereas (1301)^(1/2) in the exponential form. √1301 ≈ 36.067, 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, 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 1301 is broken down into its prime factors.
Step 1: Finding the prime factors of 1301 1301 is a prime number and cannot be broken down into smaller prime factors. Therefore, calculating 1301 using prime factorization 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: To begin with, we need to group the numbers from right to left. In the case of 1301, we need to group it as 01 and 13.
Step 2: Now, we need to find n whose square is less than or equal to 13. We can say n is ‘3’ because 3^2 = 9 is less than or equal to 13. Now the quotient is 3, and after subtracting 9 from 13, the remainder is 4.
Step 3: Bring down 01, which makes the new dividend 401. Add the old divisor with the same number 3 + 3 = 6, which will be our new divisor placeholder.
Step 4: Now, we need to find a digit x such that 6x * x ≤ 401. Let us consider x as 6, now 66 * 6 = 396.
Step 5: Subtract 396 from 401, and the remainder is 5.
Step 6: Since the dividend is smaller than the divisor, we add a decimal point to the quotient and bring down 00, making the new dividend 500.
Step 7: Now, find the new divisor that is 606y * y ≤ 5000. Let us consider y as 8, now 608 * 8 = 4864.
Step 8: Subtract 4864 from 5000, and the remainder is 136. Step 9: The quotient is now 36.08. Continue doing these steps until you achieve the desired decimal precision.
So the square root of √1301 ≈ 36.067.
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 1301 using the approximation method.
Step 1: Find the closest perfect squares of √1301. The smallest perfect square less than 1301 is 1296, and the largest perfect square greater than 1301 is 1369. √1301 falls somewhere between 36 and 37.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula (1301 - 1296) / (1369 - 1296) ≈ 0.067 Using the formula, we identified the decimal point of our square root. Add this value to the smaller whole number: 36 + 0.067 = 36.067. Thus, the square root of 1301 is approximately 36.067.
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods. 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 √1301?
The area of the square is approximately 1693.32 square units.
The area of the square = side^2.
The side length is given as √1301.
Area of the square = side^2 = √1301 × √1301 ≈ 36.067 × 36.067 ≈ 1693.32.
Therefore, the area of the square box is approximately 1693.32 square units.
A square-shaped building measuring 1301 square feet is built; if each of the sides is √1301, what will be the square feet of half of the building?
Approximately 650.5 square feet.
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1301 by 2 = 650.5.
So half of the building measures approximately 650.5 square feet.
Calculate √1301 × 5.
Approximately 180.335.
The first step is to find the square root of 1301, which is approximately 36.067, then multiply 36.067 by 5.
So 36.067 × 5 ≈ 180.335.
What will be the square root of (1300 + 1)?
The square root is approximately 36.067.
To find the square root, we need to find the sum of (1300 + 1). 1300 + 1 = 1301, and then √1301 ≈ 36.067.
Therefore, the square root of (1300 + 1) is approximately ±36.067.
Find the perimeter of the rectangle if its length ‘l’ is √1301 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle to be approximately 172.134 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1301 + 50) ≈ 2 × (36.067 + 50) ≈ 2 × 86.067 ≈ 172.134 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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