Square Root of 24336
2026-02-28 09:45 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 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 24336.

What is the Square Root of 24336?

The square root is the inverse of the square of the number. 24336 is a perfect square. The square root of 24336 is expressed in both radical and exponential form. In the radical form, it is expressed as √24336, whereas (24336)(1/2) in the exponential form. √24336 = 156, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 24336

The prime factorization method is used for perfect square numbers. For non-perfect square numbers, methods like the long-division method and approximation method are used. Here, we will use the prime factorization method since 24336 is a perfect square.

Square Root of 24336 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now, let us look at how 24336 is broken down into its prime factors.

Step 1: Finding the prime factors of 24336 Breaking it down, we get 2 × 2 × 2 × 2 × 3 × 3 × 13 × 13: 24 × 32 × 132

Step 2: Now we found the prime factors of 24336. The second step is to make pairs of those prime factors. Since 24336 is a perfect square, we can perfectly group the digits into pairs: (2 × 2) × (2 × 2) × (3) × (3) × (13) × (13)

Step 3: Taking one number from each pair gives us the square root of 24336. Thus, √24336 = 2 × 2 × 3 × 13 = 156.

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Square Root of 24336 by Long Division Method

The long division method is a systematic approach to finding the square root of non-perfect squares, but it can also be used for perfect squares. Here’s how you can find the square root using the long division method.

Step 1: Start by grouping the digits of 24336 from right to left in pairs: 24|336

Step 2: Find a number whose square is less than or equal to 24. The number is 4 because 4 × 4 = 16, and the remainder is 8.

Step 3: Bring down the next pair of digits, making the new dividend 8336. Double the quotient (which is 4) and write it as 8, leaving space for the next digit of the new divisor 8_.

Step 4: Find a digit to fill the blank in 8_ such that 8_n × n is less than or equal to 8336. The digit is 3, giving 83 × 3 = 249, and the remainder is 0.

Step 5: Repeat the process if necessary. Here, the square root of 24336 is 156 exactly, with no remainder.

Square Root of 24336 by Approximation Method

Approximation is generally used for non-perfect squares. However, knowing the approximation method is useful.

Step 1: Identify the perfect squares closest to 24336. The perfect square closest to 24336 is exactly 24336 since it is a perfect square.

Step 2: Since 24336 is already a perfect square, we find that √24336 = 156 directly.

Common Mistakes and How to Avoid Them in the Square Root of 24336

Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in methods. Now, let us look at a few of those mistakes that students tend to make 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 √24336?

Okay, lets begin

The area of the square is 24336 square units.

Explanation

The area of the square = side2.

The side length is given as √24336.

Area of the square = side2 = √24336 × √24336 = 156 × 156 = 24336.

Therefore, the area of the square box is 24336 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 24336 square feet is built; if each of the sides is √24336, what will be the square feet of half of the building?

Okay, lets begin

12168 square feet

Explanation

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

Dividing 24336 by 2, we get 12168.

So half of the building measures 12168 square feet.

Well explained 👍

Problem 3

Calculate √24336 × 5.

Okay, lets begin

780

Explanation

The first step is to find the square root of 24336, which is 156.

The second step is to multiply 156 by 5.

So 156 × 5 = 780.

Well explained 👍

Problem 4

What will be the square root of (24336 + 64)?

Okay, lets begin

The square root is 158.

Explanation

To find the square root, we need to find the sum of (24336 + 64).

24336 + 64 = 24400, and then √24400 = 158.

Therefore, the square root of (24336 + 64) is ±158.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √24336 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is 388 units.

Explanation

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

Perimeter = 2 × (√24336 + 38) = 2 × (156 + 38) = 2 × 194 = 388 units.

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FAQ on Square Root of 24336

1.What is √24336 in its simplest form?

The prime factorization of 24336 is 2 × 2 × 2 × 2 × 3 × 3 × 13 × 13, so the simplest form of √24336 = √(24 × 32 × 132) = 156.

2.Mention the factors of 24336.

Factors of 24336 include 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 78, 104, 117, 156, 234, 312, 468, 624, 936, 1218, 1872, 2433, 3744, 4866, 7299, 9720, and 24336.

3.Calculate the square of 24336.

We get the square of 24336 by multiplying the number by itself, that is 24336 × 24336 = 592974336.

4.Is 24336 a prime number?

24336 is not a prime number, as it has more than two factors.

5.24336 is divisible by?

24336 has many factors, including 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 78, 104, 117, 156, 234, 312, 468, 624, 936, 1218, 1872, 2433, 3744, 4866, 7299, 9720, and 24336.

Important Glossaries for the Square Root of 24336

  • Square root: A square root is the inverse of a square. Example: 122 = 144 and the inverse of the square is the square root, which is √144 = 12.
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 4, 9, 16, 25, etc., are perfect squares.
  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
  • Exponent: An exponent refers to the number of times a number is multiplied by itself. For example, in 23, 3 is the exponent, indicating 2 × 2 × 2.
  • Divisor: A divisor is a number by which another number is to be divided. For example, in 12 ÷ 3 = 4, 3 is the divisor.

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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.

Fun Fact

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