Square Root of 20000
2026-02-28 08:41 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-20000

462 Learners

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 20000.

What is the Square Root of 20000?

The square root is the inverse of the square of the number. 20000 is not a perfect square. The square root of 20000 is expressed in both radical and exponential form. In the radical form, it is expressed as √20000, whereas (20000)(1/2) in the exponential form. √20000 ≈ 141.421, 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 20000

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:

  1. Prime factorization method
  2. Long division method
  3. Approximation method

Square Root of 20000 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 20000 is broken down into its prime factors.

Step 1: Finding the prime factors of 20000 Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5: 24 x 55

Step 2: Now we found out the prime factors of 20000. The second step is to make pairs of those prime factors. Since 20000 is not a perfect square, therefore the digits of the number can’t be grouped in a perfect pair.

Therefore, calculating √20000 using prime factorization is impossible.

Explore Our Programs

Square Root of 20000 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 20000, we need to group it as 000 and 20.

Step 2: Now we need to find n whose square is 20. We can say n as ‘4’ because 4 × 4 is lesser than or equal to 20. Now the quotient is 4, and after subtracting 16 from 20, the remainder is 4.

Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 4 + 4 to get 8, which will be our new divisor.

Step 4: The new divisor will be 8n. Now we need to find the value of n.

Step 5: The next step is finding 8n × n ≤ 400. Let us consider n as 5, now 8 × 5 × 5 = 400.

Step 6: Subtract 400 from 400, the difference is 0, and the quotient is 45.

Step 7: Since the dividend is zero, we have our quotient as 141.42. So the square root of √20000 ≈ 141.42

Square Root of 20000 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 20000 using the approximation method.

Step 1: Now we have to find the closest perfect square of √20000. The smallest perfect square of 20000 is 19600 (1402) and the largest perfect square of 20000 is 20449 (1432). √20000 falls somewhere between 140 and 143.

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square)

Going by the formula (20000 - 19600) ÷ (20449 - 19600) ≈ 0.42 Using the formula, we identified the decimal point of our square root.

The next step is adding the value we got initially to the decimal number which is 140 + 0.42 ≈ 140.42, so the square root of 20000 is approximately 141.42.

Common Mistakes and How to Avoid Them in the Square Root of 20000

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.

Download Worksheets

Problem 1

Can you help Max find the area of a square box if its side length is given as √20000?

Okay, lets begin

The area of the square is 20000 square units.

Explanation

The area of the square = side2.

The side length is given as √20000.

Area of the square = side2 = √20000 × √20000 = 20000.

Therefore, the area of the square box is 20000 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 20000 square feet is built; if each of the sides is √20000, what will be the square feet of half of the building?

Okay, lets begin

10000 square feet

Explanation

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

Dividing 20000 by 2 gives us 10000.

So half of the building measures 10000 square feet.

Well explained 👍

Problem 3

Calculate √20000 × 5.

Okay, lets begin

707.106

Explanation

The first step is to find the square root of 20000,

which is approximately 141.421, then multiply 141.421 by 5.

So, 141.421 × 5 ≈ 707.106.

Well explained 👍

Problem 4

What will be the square root of (19800 + 200)?

Okay, lets begin

The square root is 141.421.

Explanation

To find the square root, we need to find the sum of (19800 + 200).

19800 + 200 = 20000, and then √20000 ≈ 141.421.

Therefore, the square root of (19800 + 200) is approximately 141.421.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √20000 units and the width ‘w’ is 50 units.

Okay, lets begin

The perimeter of the rectangle is 382.842 units.

Explanation

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

Perimeter = 2 × (√20000 + 50) ≈ 2 × (141.421 + 50) ≈ 2 × 191.421 ≈ 382.842 units.

Well explained 👍

FAQ on Square Root of 20000

1.What is √20000 in its simplest form?

The prime factorization of 20000 is 24 × 55,

so the simplest form of √20000 = √(24 × 55).

2.Mention the factors of 20000.

Factors of 20000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 4000, 5000, 10000, and 20000.

3.Calculate the square of 20000.

We get the square of 20000 by multiplying the number by itself, that is 20000 × 20000 = 400000000.

4.Is 20000 a prime number?

20000 is not a prime number, as it has more than two factors.

5.20000 is divisible by?

20000 has many factors; those are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 4000, 5000, 10000, and 20000.

Important Glossaries for the Square Root of 20000

  • Square root: A square root is the inverse of a square. Example: 42 = 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.
  • Perfect square: A perfect square is a number that is the square of an integer. For example: 16 is a perfect square because it is 42.
  • Long division method: A mathematical procedure used to find the square root of non-perfect squares through a step-by-step division process.
  • Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 32.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.