Square Root of 13284
2026-02-28 10:21 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-13284

223 Learners

Last updated on August 5, 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 13284.

What is the Square Root of 13284?

The square root is the inverse of the square of the number. 13284 is not a perfect square. The square root of 13284 is expressed in both radical and exponential form. In the radical form, it is expressed as √13284, whereas (13284)(1/2) in the exponential form. The square root of 13284 is approximately 115.248, 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 13284

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:

  1. Prime factorization method
  2. Long division method
  3. Approximation method

Square Root of 13284 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 13284 is broken down into its prime factors:

Step 1: Finding the prime factors of 13284 Breaking it down, we get 2 x 2 x 3 x 3 x 3 x 7 x 11.

Step 2: Now we found out the prime factors of 13284. The second step is to make pairs of those prime factors. Since 13284 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating 13284 using prime factorization is impossible.

Explore Our Programs

Square Root of 13284 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 13284, we need to group it as 84 and 132.

Step 2: Now we need to find n whose square is closest to 132. We can say n as ‘11’ because 11 x 11 is 121, which is less than or equal to 132. Now the quotient is 11, and after subtracting 121 from 132, the remainder is 11.

Step 3: Now let us bring down 84 to make it the new dividend, which becomes 1184. Add the old divisor with the same number 11 + 11 to get 22, which will be our new divisor.

Step 4: The new divisor will be the sum of the previous divisor and the quotient. Now we get 22n as the new divisor, and we need to find the value of n.

Step 5: The next step is finding 22n x n ≤ 1184. Let us consider n as 5, now 225 x 5 = 1125.

Step 6: Subtracting 1125 from 1184 gives us a difference of 59, and the quotient is 115.

Step 7: 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. The new dividend becomes 5900.

Step 8: Now we need to find the new divisor, which is 1154, because 1154 x 4 = 4616.

Step 9: Subtracting 4616 from 5900 gives a result of 1284.

Step 10: Now the quotient is 115.2.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero. So the square root of √13284 is approximately 115.25.

Square Root of 13284 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 13284 using the approximation method.

Step 1: Now we have to find the closest perfect squares of √13284. The smallest perfect square less than 13284 is 12996 (1142), and the largest perfect square greater than 13284 is 13689 (1172). √13284 falls somewhere between 114 and 117.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square)

Using the formula (13284 - 12996) ÷ (13689 - 12996) = 288 ÷ 693 ≈ 0.415 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 114 + 0.415 = 114.415, so the square root of 13284 is approximately 115.25.

Common Mistakes and How to Avoid Them in the Square Root of 13284

Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Now let us look at a few of those mistakes in detail.

Download Worksheets

Problem 1

Can you help Max find the area of a square box if its side length is given as √14400?

Okay, lets begin

The area of the square is 14400 square units.

Explanation

The area of the square = side2.

The side length is given as √14400.

Area of the square = side2 = √14400 x √14400 = 120 x 120 = 14400.

Therefore, the area of the square box is 14400 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 13284 square feet is built; if each of the sides is √13284, what will be the square feet of half of the building?

Okay, lets begin

6642 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 13284 by 2 gives us 6642.

So half of the building measures 6642 square feet.

Well explained 👍

Problem 3

Calculate √13284 x 5.

Okay, lets begin

576.24

Explanation

The first step is to find the square root of 13284, which is approximately 115.25.

The second step is to multiply 115.25 by 5.

So 115.25 x 5 = 576.24.

Well explained 👍

Problem 4

What will be the square root of (14400 + 25)?

Okay, lets begin

The square root is 120.1.

Explanation

To find the square root, we need to find the sum of (14400 + 25).

14400 + 25 = 14425, and then √14425 ≈ 120.1.

Therefore, the square root of (14400 + 25) is approximately ±120.1.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √14400 units and the width ‘w’ is 50 units.

Okay, lets begin

We find the perimeter of the rectangle as 340 units.

Explanation

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

Perimeter = 2 × (√14400 + 50) = 2 × (120 + 50) = 2 × 170 = 340 units.

Well explained 👍

FAQ on Square Root of 13284

1.What is √13284 in its simplest form?

The prime factorization of 13284 is 2 x 2 x 3 x 3 x 3 x 7 x 11, so the simplest form of √13284 = √(2 x 2 x 3 x 3 x 3 x 7 x 11).

2.Mention the factors of 13284.

Factors of 13284 include 1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 18, 21, 22, 28, 33, 36, 42, 44, 49, 63, 66, 77, 84, 98, 126, 132, 154, 189, 198, 231, 252, 308, 363, 396, 462, 693, 924, 1323, 1848, 2646, 3969, 5292, 13284.

3.Calculate the square of 13284.

We get the square of 13284 by multiplying the number by itself, that is 13284 x 13284 = 176947456.

4.Is 13284 a prime number?

13284 is not a prime number, as it has more than two factors.

5.13284 is divisible by?

13284 has many factors; those include 1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 18, 21, 22, 28, 33, 36, 42, 44, 49, 63, 66, 77, 84, 98, 126, 132, 154, 189, 198, 231, 252, 308, 363, 396, 462, 693, 924, 1323, 1848, 2646, 3969, 5292, and 13284.

Important Glossaries for the Square Root of 13284

  • Square root: A square root is the inverse of squaring a number. Example: 42 = 16 and the inverse of squaring is the square root, so √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, the positive square root is more commonly used in the real world. It is known as the principal square root.
  • Prime factorization: It is the method of expressing a number as the product of its prime factors.
  • Decimal: A decimal is a number that has a whole number part and a fractional part, separated by a decimal point, such as 7.86, 8.65, and 9.42.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.