Square Root of 1350
2026-02-28 13:42 Diff
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Last updated on August 5, 2025

If a number is multiplied by the same number, the result is a square. The inverse operation is finding the square root. The square root is used in various fields such as architecture, finance, etc. Here, we will discuss the square root of 1350.

What is the Square Root of 1350?

The square root is the inverse of the square of a number. 1350 is not a perfect square. The square root of 1350 is expressed in both radical and exponential forms. In radical form, it is expressed as √1350, whereas in exponential form it is (1350)^(1/2). √1350 ≈ 36.7423, 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 1350

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 1350 by Prime Factorization Method

The prime factorization of a number involves expressing it as a product of prime factors. Now let us look at how 1350 is broken down into its prime factors:

Step 1: Finding the prime factors of 1350

Breaking it down, we get 2 x 3 x 3 x 3 x 5 x 5: 2¹ x 3³ x 5²

Step 2: Now we found the prime factors of 1350. The next step is to make pairs of those prime factors. Since 1350 is not a perfect square, we cannot pair all the digits completely. Therefore, calculating √1350 using only prime factorization is not possible.

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Square Root of 1350 by Long Division Method

The long division method is particularly useful for non-perfect square numbers. In this method, we 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 1350, we group it as 50 and 13.

Step 2: Find n whose square is 13. We can say n is '3' because 3 x 3 = 9, which is less than 13. The quotient is 3, and after subtracting 9 from 13, the remainder is 4.

Step 3: Bring down 50, making the new dividend 450. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

Step 4: The new divisor is 6n. We need to find a value of n such that 6n x n ≤ 450. Let n be 7, then 67 x 7 = 469.

Step 5: Subtracting 469 from 450, we get -19. We adjust n to 6, making 66 x 6 = 396.

Step 6: Subtract 396 from 450, resulting in a remainder of 54. The quotient is 36.

Step 7: Since the dividend is less than the divisor, we add a decimal point and two zeroes to the dividend, making it 5400.

Step 8: Find the new divisor, 732, because 732 x 7 = 5124. Subtracting gives us a remainder of 276.

Step 9: The quotient continues with decimal places, approximating to 36.74.

Square Root of 1350 by Approximation Method

Approximation is another way to find square roots easily. Let us learn how to find the square root of 1350 using the approximation method.

Step 1: Identify the closest perfect squares to 1350. The smallest perfect square less than 1350 is 1296, and the largest perfect square greater than 1350 is 1369. √1350 falls between 36 and 37.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (1350 - 1296) / (1369 - 1296) = 54 / 73 ≈ 0.7397 Adding the integer part, 36 + 0.7397 ≈ 36.74, so the square root of 1350 is approximately 36.74.

Common Mistakes and How to Avoid Them in the Square Root of 1350

Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let us examine some common mistakes in detail.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √1350?

Okay, lets begin

The area of the square is approximately 1822.54 square units.

Explanation

The area of the square = side².

The side length is given as √1350.

Area of the square = side² = √1350 x √1350 ≈ 36.74 x 36.74 ≈ 1822.54

Therefore, the area of the square box is approximately 1822.54 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1350 square feet is built; if each of the sides is √1350, what will be the square feet of half of the building?

Okay, lets begin

675 square feet

Explanation

Since the building is square-shaped, divide the area by 2.

1350 / 2 = 675

So half of the building measures 675 square feet.

Well explained 👍

Problem 3

Calculate √1350 x 5.

Okay, lets begin

Approximately 183.71

Explanation

First, find the square root of 1350, which is approximately 36.74.

Multiply 36.74 by 5. So, 36.74 x 5 ≈ 183.71

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Problem 4

What will be the square root of (1350 + 19)?

Okay, lets begin

The square root is approximately 37

Explanation

To find the square root, first find the sum of 1350 + 19 = 1369, and then √1369 = 37.

Therefore, the square root of (1350 + 19) is ±37.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1350 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is approximately 149.48 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√1350 + 38) ≈ 2 × (36.74 + 38) ≈ 2 × 74.74 ≈ 149.48 units.

Well explained 👍

FAQ on Square Root of 1350

1.What is √1350 in its simplest form?

The prime factorization of 1350 is 2 x 3 x 3 x 3 x 5 x 5, so the simplest form of √1350 is √(2 x 3³ x 5²).

2.Mention the factors of 1350.

Factors of 1350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, and 1350.

3.Calculate the square of 1350.

We find the square of 1350 by multiplying the number by itself, that is 1350 x 1350 = 1822500.

4.Is 1350 a prime number?

1350 is not a prime number, as it has more than two factors.

5.1350 is divisible by?

1350 has many factors; it is divisible by 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, and 1350.

Important Glossaries for the Square Root of 1350

  • Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, which is √16 = 4.
  • Irrational number: An irrational number is a number that cannot be written as a simple fraction - it goes on forever without repeating. For example, √1350 is an irrational number.
  • Prime factorization: Prime factorization is the process of expressing a number as the product of its prime numbers. For example, the prime factorization of 1350 is 2 x 3³ x 5².
  • Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
  • Approximation: Approximating a number means finding a value that is close enough to the right answer, usually with some insight. For example, the square root of 1350 is approximately 36.74.

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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.

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: He loves to play the quiz with kids through algebra to make kids love it.