Square Root of 4624
2026-02-28 12:44 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 4624.

What is the Square Root of 4624?

The square root is the inverse of the square of the number. 4624 is a perfect square. The square root of 4624 is expressed in both radical and exponential form. In the radical form, it is expressed as √4624, whereas (4624)^(1/2) in the exponential form. √4624 = 68, 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 4624

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. Let us now learn the following methods:

  • Prime factorization method
  • Long division method
  • Approximation method

Square Root of 4624 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 4624 is broken down into its prime factors.

Step 1: Finding the prime factors of 4624

Breaking it down, we get 2 × 2 × 2 × 2 × 17 × 17: 2^4 × 17^2

Step 2: Now we found out the prime factors of 4624. The second step is to make pairs of those prime factors. Since 4624 is a perfect square, we can group the factors into pairs of 2^2 × 17. Therefore, the square root of 4624 using prime factorization is 2^2 × 17 = 68.

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Square Root of 4624 by Long Division Method

The long division method is particularly used for perfect and non-perfect square numbers. In this method, we find the square root using a step-by-step division approach.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 4624, we group it as 46 and 24.

Step 2: Now we need to find a number whose square is less than or equal to 46. We can use 6 because 6 × 6 = 36, which is less than 46. Now the quotient is 6.

Step 3: Subtract 36 from 46; the remainder is 10. Bring down the next pair of digits, 24, making the new dividend 1024.

Step 4: Double the quotient and write it as the new divisor with a blank digit next to it (12_).

Step 5: Find a digit to fill the blank such that when you multiply the new divisor by this digit, the product is less than or equal to 1024. The digit is 8, making the divisor 128.

Step 6: 128 × 8 = 1024; subtracting gives a remainder of 0.

So the square root of √4624 is 68.

Square Root of 4624 by Approximation Method

The approximation method is another method for finding square roots and is an easy method to find the square root of a given number. Now let us learn how to find the square root of 4624 using the approximation method.

Step 1: Find numbers whose squares are close to 4624. The perfect squares closest to 4624 are 4624 itself. Since 4624 is a perfect square, the approximation method directly confirms the square root as 68.

Common Mistakes and How to Avoid Them in the Square Root of 4624

Students make mistakes while finding square roots, sometimes forgetting about the negative square root or skipping steps in the long division method. 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 √4624?

Okay, lets begin

The area of the square is 4624 square units.

Explanation

The area of the square = side^2.

The side length is given as √4624.

Area of the square = side^2 = √4624 × √4624 = 68 × 68 = 4624.

Therefore, the area of the square box is 4624 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 4624 square feet is built; if each of the sides is √4624, what will be the square feet of half of the building?

Okay, lets begin

2312 square feet

Explanation

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

Dividing 4624 by 2 gives us 2312.

So half of the building measures 2312 square feet.

Well explained 👍

Problem 3

Calculate √4624 × 3.

Okay, lets begin

204

Explanation

The first step is to find the square root of 4624, which is 68.

The second step is to multiply 68 by 3.

So 68 × 3 = 204.

Well explained 👍

Problem 4

What will be the square root of (4000 + 624)?

Okay, lets begin

The square root is 68.

Explanation

To find the square root, we need to find the sum of (4000 + 624). 4000 + 624 = 4624, and then √4624 = 68.

Therefore, the square root of (4000 + 624) is ±68.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √4624 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is 212 units.

Explanation

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

Perimeter = 2 × (√4624 + 38) = 2 × (68 + 38) = 2 × 106 = 212 units.

Well explained 👍

FAQ on Square Root of 4624

1.What is √4624 in its simplest form?

The prime factorization of 4624 is 2 × 2 × 2 × 2 × 17 × 17, so the simplest form of √4624 = √(2^4 × 17^2) = 68.

2.Mention the factors of 4624.

Factors of 4624 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272, 289, 578, 1156, 2312, and 4624.

3.Calculate the square of 68.

We get the square of 68 by multiplying the number by itself, that is, 68 × 68 = 4624.

4.Is 4624 a prime number?

4624 is not a prime number, as it has more than two factors.

5.4624 is divisible by?

4624 has many factors; those are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272, 289, 578, 1156, 2312, and 4624.

Important Glossaries for the Square Root of 4624

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
  • 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 can be expressed as the square of an integer. For example, 4624 is a perfect square because it is 68^2.
  • Exponent: An exponent refers to the number of times a number is multiplied by itself. For example, 2^3 = 2 × 2 × 2 = 8.
  • Divisor: A divisor is a number by which another number is divided. For example, in 4624 ÷ 68 = 68, 68 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.