Square Root of 588
2026-02-28 10:34 Diff
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Last updated on September 30, 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 such as vehicle design, finance, etc. Here, we will discuss the square root of 588.

What is the Square Root of 588?

The square root is the inverse of the square of the number. 588 is not a perfect square. The square root of 588 is expressed in both radical and exponential form. In the radical form, it is expressed as √588, whereas (588)^(1/2) in the exponential form. √588 ≈ 24.2487, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 588

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 588 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 588 is broken down into its prime factors.

Step 1: Finding the prime factors of 588 Breaking it down, we get 2 x 2 x 3 x 7 x 7: 2^2 x 3 x 7^2.

Step 2: Now we found out the prime factors of 588. The second step is to make pairs of those prime factors. Since 588 is not a perfect square, the digits of the number can’t be grouped in perfect pairs for a square root without leaving a remainder.

Therefore, calculating 588 using prime factorization results in an approximate square root.

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Square Root of 588 by Long Division Method

The long division method is particularly used for 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 588, we group it as 88 and 5.

Step 2: Now we need to find n whose square is ≤ 5. We can say n as ‘2’ because 2 x 2 = 4 is lesser than or equal to 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.

Step 3: Now let us bring down 88, making the new dividend 188. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 188. Let’s consider n as 4, then 44 x 4 = 176.

Step 5: Subtract 176 from 188; the difference is 12, and the quotient is 24.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point, allowing us to add two zeros to the dividend. Now the new dividend is 1200.

Step 7: The new divisor should be 244 because 244 x 4 = 976, which is less than 1200.

Step 8: Subtracting 976 from 1200 gives us a remainder of 224.

Step 9: Continue this process until we reach a desired level of decimal precision.

The approximate square root of 588 is 24.248.

Square Root of 588 by Approximation Method

The approximation method is another method for finding 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 588 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √588. The closest perfect squares are 576 (24^2) and 625 (25^2), so √588 falls somewhere between 24 and 25.

Step 2: Now we apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (588 - 576) / (625 - 576) = 12 / 49 ≈ 0.245. Adding this to 24 gives us 24 + 0.245 = 24.245, so the square root of 588 is approximately 24.245.

Common Mistakes and How to Avoid Them in the Square Root of 588

Students often make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the long division method. Now 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 √588?

Okay, lets begin

The area of the square is approximately 345.504 square units.

Explanation

The area of the square = side^2.

The side length is given as √588.

Area of the square = side^2 = √588 x √588 ≈ 24.2487 x 24.2487 ≈ 588.

Therefore, the area of the square box is approximately 588 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 588 square feet is built; if each of the sides is √588, what will be the square feet of half of the building?

Okay, lets begin

294 square feet

Explanation

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

Dividing 588 by 2 gives us 294.

So, half of the building measures 294 square feet.

Well explained 👍

Problem 3

Calculate √588 x 5.

Okay, lets begin

121.2435

Explanation

The first step is to find the square root of 588, which is approximately 24.2487.

The second step is to multiply 24.2487 by 5. So, 24.2487 x 5 ≈ 121.2435.

Well explained 👍

Problem 4

What will be the square root of (576 + 12)?

Okay, lets begin

The square root is 24.

Explanation

To find the square root, first find the sum of (576 + 12). 576 + 12 = 588, and then √588 ≈ 24.2487.

Therefore, the square root of (576 + 12) is approximately ±24.2487.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √588 units and the width ‘w’ is 38 units.

Okay, lets begin

The perimeter of the rectangle is approximately 124.4974 units.

Explanation

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

Perimeter = 2 × (√588 + 38) ≈ 2 × (24.2487 + 38) ≈ 2 × 62.2487 ≈ 124.4974 units.

Well explained 👍

FAQ on Square Root of 588

1.What is √588 in its simplest form?

The prime factorization of 588 is 2 x 2 x 3 x 7 x 7, so the simplest form of √588 is √(2^2 x 3 x 7^2) = 2 x 7 x √3 ≈ 14√3.

2.Mention the factors of 588.

Factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, and 588.

3.Calculate the square of 588.

We get the square of 588 by multiplying the number by itself, that is, 588 x 588 = 345,744.

4.Is 588 a prime number?

5.588 is divisible by?

588 has many factors; those are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, and 588.

Important Glossaries for the Square Root of 588

  • Square root: A square root is the inverse of a square. For example, 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.
  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.
  • Principal square root: A number has both positive and negative square roots; however, the positive square root is more prominent due to its uses in the real world. This is why it is also known as the principal square root.
  • Factors: Factors are numbers that can be multiplied together to get another number. For example, factors of 588 are 1, 2, 3, 4, 6, 7, etc.
  • Approximation: An approximation is a value or number that is close to the exact value but not exact. For example, the approximate square root of 588 is 24.2487.

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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.

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