Square Root of 3364
2026-02-28 15:50 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 3364.

What is the Square Root of 3364?

The square root is the inverse of the square of the number. 3364 is a perfect square. The square root of 3364 is expressed in both radical and exponential form. In the radical form, it is expressed as √3364, whereas (3364)^(1/2) in the exponential form. √3364 = 58, 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 3364

The prime factorization method is used for perfect square numbers. 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 3364 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 3364 is broken down into its prime factors.

Step 1: Finding the prime factors of 3364 Breaking it down, we get 2 x 2 x 29 x 29: 2^2 x 29^2

Step 2: Now we found out the prime factors of 3364. The second step is to make pairs of those prime factors. Since 3364 is a perfect square, the digits of the number can be grouped in pairs. Therefore, √3364 = 2 x 29 = 58.

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Square Root of 3364 by Long Division Method

The long division method is particularly used for both perfect and 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 3364, we group it as 33 and 64.

Step 2: Now we need to find n whose square is ≤ 33. We can say n is ‘5’ because 5 x 5 = 25 is less than 33. The quotient is 5, and the remainder is 33 - 25 = 8.

Step 3: Bring down 64, making the new dividend 864. Add the old divisor with the same number, 5 + 5, to get 10, which becomes the new divisor.

Step 4: Find n such that 10n x n ≤ 864. Consider n as 8, so 108 x 8 = 864.

Step 5: Subtract 864 from 864; the remainder is 0. So, the square root of √3364 is 58.

Square Root of 3364 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. Now let us learn how to find the square root of 3364 using the approximation method.

Step 1: Identify the closest perfect square of √3364. 3364 is a perfect square, so the closest perfect square is itself. √3364 falls exactly on 58.

Step 2: Since 3364 is a perfect square, no further approximation is necessary. √3364 = 58.

Common Mistakes and How to Avoid Them in the Square Root of 3364

Students do make mistakes while finding the square root, like 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.

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Problem 1

Can you help Max find the area of a square box if its side length is given as √3364?

Okay, lets begin

The area of the square is 3364 square units.

Explanation

The area of the square = side^2.

The side length is given as √3364.

Area of the square = side^2 = √3364 x √3364 = 58 x 58 = 3364.

Therefore, the area of the square box is 3364 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 3364 square feet is built; if each of the sides is √3364, what will be the square feet of half of the building?

Okay, lets begin

1682 square feet

Explanation

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

Dividing 3364 by 2 = 1682.

So half of the building measures 1682 square feet.

Well explained 👍

Problem 3

Calculate √3364 x 5.

Okay, lets begin

290

Explanation

The first step is to find the square root of 3364, which is 58; the second step is to multiply 58 with 5. So, 58 x 5 = 290.

Well explained 👍

Problem 4

What will be the square root of (324 + 40)?

Okay, lets begin

The square root is 19.

Explanation

To find the square root, we need to find the sum of (324 + 40).

324 + 40 = 364, and then √364 ≈ 19.052.

Therefore, the square root of (324 + 40) is approximately ±19.052.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √3364 units and the width ‘w’ is 40 units.

Okay, lets begin

We find the perimeter of the rectangle as 196 units.

Explanation

Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3364 + 40) = 2 × (58 + 40) = 2 × 98 = 196 units.

Well explained 👍

FAQ on Square Root of 3364

1.What is √3364 in its simplest form?

The prime factorization of 3364 is 2^2 x 29^2, so the simplest form of √3364 = 2 x 29 = 58.

2.Mention the factors of 3364.

Factors of 3364 are 1, 2, 4, 29, 58, 116, 841, 1682, and 3364.

3.Calculate the square of 3364.

We get the square of 3364 by multiplying the number by itself, that is 3364 x 3364 = 11,318,896.

4.Is 3364 a prime number?

3364 is not a prime number, as it has more than two factors.

5.3364 is divisible by?

3364 has many factors; those are 1, 2, 4, 29, 58, 116, 841, 1682, and 3364.

Important Glossaries for the Square Root of 3364

  • Square root: A square root is the inverse of a square. Example: 6^2 = 36 and the inverse of the square is the square root that is √36 = 6.
  • 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.
  • Perfect square: A perfect square is a number that is the square of an integer. Example: 9 is a perfect square because it is 3^2.
  • Prime factorization: The expression of a number as a product of its prime factors.
  • Long division method: A method used to find the square root of both perfect and non-perfect squares through step-by-step division.

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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.