Square Root of 11664
2026-02-28 10:47 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 11664.

What is the Square Root of 11664?

The square root is the inverse of the square of the number. 11664 is a perfect square. The square root of 11664 can be expressed in both radical and exponential form. In the radical form, it is expressed as √11664, whereas in the exponential form it is expressed as (11664)^(1/2). √11664 = 108, 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 11664

The prime factorization method is used for perfect square numbers. For non-perfect square numbers, the long-division method and approximation method are often used. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 11664 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 11664 is broken down into its prime factors.

Step 1: Finding the prime factors of 11664.

Breaking it down, we get 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3: 2^4 x 3^6

Step 2: Now we found out the prime factors of 11664. The second step is to make pairs of those prime factors. Since 11664 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating √11664 using prime factorization is possible.

Step 3: Pairing the factors, we get (2^2) x (3^3). Taking one factor from each pair, we find the square root: 2 x 3 x 3 = 108.

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Square Root of 11664 by Long Division Method

The long division method is particularly useful for non-perfect square numbers. However, it can also be applied to perfect squares. 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 11664, we need to group it as 64 and 116.

Step 2: Now we need to find n whose square is closest to the first group. We can say n as ‘10’ because 10 x 10 is 100, which is lesser than or equal to 116. Now the quotient is 10, and after subtracting 100 from 116, the remainder is 16.

Step 3: Now let us bring down 64, which is the new dividend. Add the old divisor with the same number, 10 + 10, we get 20, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 20n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 20n × n ≤ 1664. Let us consider n as 8, now 208 x 8 = 1664.

Step 6: Subtracting 1664 from 1664 gives the remainder as 0.

Step 7: The quotient is 108, and since the remainder is zero, the process ends here.

So, the square root of √11664 is 108.

Square Root of 11664 by Approximation Method

The approximation method is another method for finding the square roots; it is an easy method to find the square root of a given number. However, since 11664 is a perfect square, the approximation method is not necessary in this case.

Common Mistakes and How to Avoid Them in the Square Root of 11664

Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division 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 √11664?

Okay, lets begin

The area of the square is 11664 square units.

Explanation

The area of the square = side².

The side length is given as √11664.

Area of the square = side² = √11664 x √11664 = 108 x 108 = 11664.

Therefore, the area of the square box is 11664 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 11664 square feet is built; if each of the sides is √11664, what will be the square feet of half of the building?

Okay, lets begin

5832 square feet

Explanation

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

Dividing 11664 by 2, we get 5832.

So, half of the building measures 5832 square feet.

Well explained 👍

Problem 3

Calculate √11664 x 5.

Okay, lets begin

540

Explanation

The first step is to find the square root of 11664, which is 108.

The second step is to multiply 108 with 5.

So, 108 x 5 = 540.

Well explained 👍

Problem 4

What will be the square root of (11600 + 64)?

Okay, lets begin

The square root is 108.

Explanation

To find the square root, we need to find the sum of (11600 + 64). 11600 + 64 = 11664, and then √11664 = 108.

Therefore, the square root of (11600 + 64) is ±108.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √11664 units and the width ‘w’ is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as 292 units.

Explanation

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

Perimeter = 2 × (√11664 + 38) = 2 × (108 + 38) = 2 × 146 = 292 units.

Well explained 👍

FAQ on Square Root of 11664

1.What is √11664 in its simplest form?

The prime factorization of 11664 is 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3, so the simplest form of √11664 = 108.

2.Mention the factors of 11664.

Factors of 11664 include 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 432, 648, 972, 1296, 1944, 3888, 5832, and 11664.

3.Calculate the square of 108.

We get the square of 108 by multiplying the number by itself, that is 108 x 108 = 11664.

4.Is 11664 a prime number?

11664 is not a prime number, as it has more than two factors.

5.11664 is divisible by?

11664 has many factors; those are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 432, 648, 972, 1296, 1944, 3888, 5832, and 11664.

Important Glossaries for the Square Root of 11664

  • Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, 108 x 108 = 11664, thus √11664 = 108.
     
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 11664 is a perfect square because it equals 108 squared.
     
  • Rational number: A rational number can be expressed as a fraction with integer values in the numerator and a non-zero integer in the denominator. For example, 108 is a rational number.
     
  • Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 11664 is 2^4 x 3^6.
     
  • Factor: A factor is a number that divides another number without leaving a remainder. For example, 108 is a factor of 11664.

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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.