124 LearnersLast updated on May 26th, 2025
Square Root of 1313
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.
What is 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.
Finding the Square Root of 1313
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:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1313 by Prime Factorization Method
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.
Square Root of 1313 by Long Division Method
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.
Square Root of 1313 by Approximation Method
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.
Common Mistakes and How to Avoid Them in the Square Root of 1313
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.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.
For example: √50 = 7.07, there is also -7.07 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12+24) = √12 + √24 is the wrong method of using roots.
The right way of using roots is √(12+24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is wrong, the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them keep away from mistakes.
For example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1313 Examples
Problem 1
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.
Explanation
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.
Problem 2
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
Explanation
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.
Problem 3
Calculate √1313 × 4.
144.9444
Explanation
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.
Problem 4
What will be the square root of (1300 + 13)?
The square root is approximately 36.2361.
Explanation
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.
Problem 5
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.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1300 + 13) ≈ 2 × (36.0555 + 13) = 2 × 49.0555 ≈ 98.111 units.
FAQ on Square Root of 1313
1.What is √1313 in its simplest form?
2.Mention the factors of 1313.
3.Calculate the square of 1313.
4.Is 1313 a prime number?
5.1313 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 1313?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 1313?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 1313
- Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that is, √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, q is not equal to zero and p and q are integers.
- Prime factorization: This is the process of breaking down a number into its prime factors.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Long division method: A process of finding the square root of non-perfect squares by using the long division technique.
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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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