Square Root of 8464
2026-02-28 14:01 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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 8464.

What is the Square Root of 8464?

The square root is the inverse of the square of the number. 8464 is a perfect square. The square root of 8464 is expressed in both radical and exponential form. In the radical form, it is expressed as √8464, whereas (8464)^(1/2) in the exponential form. √8464 = 92, 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 8464

The prime factorization method is used for perfect square numbers. The long division method and approximation method can also be used to find square roots. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 8464 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 8464 is broken down into its prime factors.

Step 1: Finding the prime factors of 8464 Breaking it down, we get 2 x 2 x 2 x 2 x 13 x 13: 2^4 x 13^2

Step 2: Now we found out the prime factors of 8464. The next step is to make pairs of those prime factors. Since 8464 is a perfect square, we can group the digits into pairs. Therefore, calculating 8464 using prime factorization is possible.

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Square Root of 8464 by Long Division Method

The long division method is particularly useful for non-perfect square numbers, but it can also confirm results for 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 8464, we group it as 84 and 64.

Step 2: Find a number whose square is less than or equal to 84. This is 9 because 9 x 9 = 81.

Step 3: The quotient is 9. Subtract 81 from 84, the remainder is 3. Bring down the next pair, 64, to make the new dividend 364.

Step 4: Double the quotient and use it as part of the new divisor. So, 9 x 2 = 18.

Step 5: Find a digit n such that 18n x n is less than or equal to 364. Here, n is 2, because 182 x 2 = 364.

Step 6: Subtract 364 from 364 to get a remainder of 0. Since there's no remainder, the quotient is 92, confirming √8464 = 92.

Square Root of 8464 by Approximation Method

The approximation method is an easy method for finding the square roots of non-perfect squares but can confirm perfect squares by showing proximity to calculated roots.

Step 1: Find the closest perfect square numbers around 8464. Since 8464 is a perfect square, its square root is exactly between 91 and 93.

Step 2: Verify by calculating: 91^2 = 8281 and 93^2 = 8649. Since 8464 is exactly between these, it confirms √8464 = 92.

Common Mistakes and How to Avoid Them in the Square Root of 8464

Students can make mistakes while finding the square root, such as forgetting about the negative square root, or skipping steps in methods. Let us look at a few of these 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 √8464?

Okay, lets begin

The area of the square is 8464 square units.

Explanation

The area of the square = side^2. The side length is given as √8464. Area of the square = side^2 = √8464 x √8464 = 92 x 92 = 8464. Therefore, the area of the square box is 8464 square units.

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Problem 2

A square-shaped building measuring 8464 square feet is built; if each of the sides is √8464, what will be the square feet of half of the building?

Okay, lets begin

4232 square feet

Explanation

We can divide the given area by 2 as the building is square-shaped. Dividing 8464 by 2 = we get 4232. So half of the building measures 4232 square feet.

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Problem 3

Calculate √8464 x 5.

Okay, lets begin

460

Explanation

The first step is to find the square root of 8464, which is 92. The second step is to multiply 92 by 5. So 92 x 5 = 460.

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Problem 4

What will be the square root of (8464 + 36)?

Okay, lets begin

The square root is 97

Explanation

To find the square root, we need to find the sum of (8464 + 36). 8464 + 36 = 8500, and the approximate square root of 8500 is 97.07, rounded to 97. Therefore, the square root of (8464 + 36) is approximately ±97.

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Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √8464 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is 260 units.

Explanation

Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√8464 + 38) = 2 × (92 + 38) = 2 × 130 = 260 units.

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FAQ on Square Root of 8464

1.What is √8464 in its simplest form?

The prime factorization of 8464 is 2 x 2 x 2 x 2 x 13 x 13, so the simplest form of √8464 = √(2^4 x 13^2) = 92.

2.Mention the factors of 8464.

Factors of 8464 include 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 1690, 3380, 8464.

3.Calculate the square of 8464.

We get the square of 8464 by multiplying the number by itself, that is 8464 x 8464.

4.Is 8464 a prime number?

8464 is not a prime number, as it has more than two factors.

5.8464 is divisible by?

8464 has many factors; those are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 1690, 3380, and 8464.

Important Glossaries for the Square Root of 8464

  • Square root: A square root is the inverse of a square. Example: 9^2 = 81, and the inverse of the square is the square root, that is √81 = 9.
     
  • 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 number that is the square of an integer. For example, 64 is a perfect square because it is 8^2.
     
  • Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 8464 is 2^4 x 13^2.
     
  • Long division method: A method used to find the square root of a number by dividing and averaging. This is particularly useful for non-perfect squares but can confirm perfect squares.

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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.