122 LearnersLast updated on May 26th, 2025
Square Root of 1300
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 1300.
What is the Square Root of 1300?
The square root is the inverse of the square of the number. 1300 is not a perfect square. The square root of 1300 is expressed in both radical and exponential form. In the radical form, it is expressed as, √1300, whereas (1300)^(1/2) in the exponential form. √1300 ≈ 36.0555, 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 1300
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:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1300 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1300 is broken down into its prime factors:
Step 1: Finding the prime factors of 1300
Breaking it down, we get 2 x 2 x 5 x 5 x 13: 2^2 x 5^2 x 13
Step 2: Now we found out the prime factors of 1300. The second step is to make pairs of those prime factors. Since 1300 is not a perfect square, the digits of the number can’t be grouped completely in pairs. Therefore, calculating √1300 using prime factorization is not straightforward.
Square Root of 1300 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 1300, we need to group it as 00 and 13.
Step 2: Now we need to find n whose square is less than or equal to 13. We can say n as ‘3’ because 3 x 3 = 9, which is less than 13. Now the quotient is 3, and after subtracting 9 from 13, the remainder is 4.
Step 3: Now let us bring down 00, making the new dividend 400. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.
Step 4: The new divisor will be 60, and we need to find the value of n such that 60n × n ≤ 400. Let us consider n as 6. Now, 60 x 6 = 360.
Step 5: Subtract 360 from 400; the difference is 40, and the quotient thus far is 36.
Step 6: Since the dividend is less than the new divisor, we add a decimal point and bring down two zeros, making the new dividend 4000.
Step 7: Now, calculate a new divisor, 721, because 721 x 5 = 3605.
Step 8: Subtracting 3605 from 4000 gives us a remainder of 395.
Step 9: Continue these steps until you have the desired precision. The square root of √1300 is approximately 36.0555.
Square Root of 1300 by Approximation Method
The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Let us learn how to find the square root of 1300 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1300. The smallest perfect square less than 1300 is 1225, and the largest perfect square greater than 1300 is 1369. √1300 falls somewhere between 35 and 37.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula (1300 - 1225) ÷ (1369 - 1225) = 75/144 ≈ 0.52 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 + 0.0555 = 36.0555, so the square root of 1300 is approximately 36.0555.
Common Mistakes and How to Avoid Them in the Square Root of 1300
Students do make mistakes while finding the square root, such as forgetting about the negative square root, 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 has 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 the 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 the cube root and the square root constantly, as this will help them avoid 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 1300 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1300?
The area of the square is 1300 square units.
Explanation
The area of the square = side^2.
The side length is given as √1300.
Area of the square = side^2 = √1300 x √1300 = 1300.
Therefore, the area of the square box is 1300 square units.
Problem 2
A square-shaped building measuring 1300 square feet is built; if each of the sides is √1300, what will be the square feet of half of the building?
650 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1300 by 2 = we get 650.
So half of the building measures 650 square feet.
Problem 3
Calculate √1300 x 5.
180.2775
Explanation
The first step is to find the square root of 1300, which is approximately 36.0555.
The second step is to multiply 36.0555 with 5.
So, 36.0555 x 5 ≈ 180.2775.
Problem 4
What will be the square root of (1300 + 49)?
The square root is 37.
Explanation
To find the square root, we need to find the sum of (1300 + 49). 1300 + 49 = 1349, and then √1349 ≈ 37.
Therefore, the square root of (1300 + 49) is approximately ±37.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1300 units and the width ‘w’ is 40 units.
We find the perimeter of the rectangle as 152.111 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1300 + 40) ≈ 2 × (36.0555 + 40) ≈ 2 × 76.0555 ≈ 152.111 units.
FAQ on Square Root of 1300
1.What is √1300 in its simplest form?
2.Mention the factors of 1300.
3.Calculate the square of 1300.
4.Is 1300 a prime number?
5.1300 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 1300?
8.How do technology and digital tools in India support learning Algebra and Square Root of 1300?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 1300
- Square root: A square root is the inverse of a square. Example: 4^2 = 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, where q is not equal to zero and p and q are integers.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1300 is 2^2 x 5^2 x 13.
- Long division method: A method used to find the square root of non-perfect squares by dividing the number into smaller parts and solving step by step.
Explore More algebra
About BrightChamps in India
Jaskaran Singh Saluja
About the Author
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
