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Last updated on April 7th, 2025

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Square Root of 43000

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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 43000.

Square Root of 43000 for Thai Students
Professor Greenline from BrightChamps

What is the Square Root of 43000?

The square root is the inverse of the square of the number. 43000 is not a perfect square. The square root of 43000 is expressed in both radical and exponential form. In the radical form, it is expressed as √43000, whereas (43000)^(1/2) in the exponential form. √43000 ≈ 207.364, 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.

square root of 43000

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Finding the Square Root of 43000

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are used. Let us now learn the following methods:

 

  • Prime factorization method
  • Long division method
  • Approximation method
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Square Root of 43000 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 43000 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 43000 Breaking it down, we get 2 x 2 x 2 x 5 x 5 x 5 x 43: 2^3 x 5^3 x 43

 

Step 2: Now we found out the prime factors of 43000. The second step is to make pairs of those prime factors. Since 43000 is not a perfect square, therefore the digits of the number can’t be grouped in pair.

 

Therefore, calculating 43000 using prime factorization is impossible.

Professor Greenline from BrightChamps

Square Root of 43000 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 43000, we need to group it as 00 and 430.

 

Step 2: Now we need to find n whose square is less than or equal to 430. We can say n as ‘20’ because 20 x 20 = 400 is lesser than 430. Now the quotient is 20 after subtracting 400 from 430, the remainder is 30.

 

Step 3: Now let us bring down 00 which is the new dividend. Add the old divisor with the same number, 20 + 20, we get 40 which will be our new divisor.

 

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 40n as the new divisor, we need to find the value of n.

 

Step 5: The next step is finding 40n × n ≤ 3000. Let us consider n as 7, now 407 x 7 = 2849.

 

Step 6: Subtract 2849 from 3000, the difference is 151, and the quotient is 207.

 

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 15100.

 

Step 8: Now we need to find the new divisor that is 414 because 414 x 3 = 1242.

 

Step 9: Subtracting 1242 from 15100 we get the result 25858.

 

Step 10: Now the quotient is 207.3.

 

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

 

So the square root of √43000 ≈ 207.36.

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Square Root of 43000 by Approximation Method

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 43000 using the approximation method.

 

Step 1: Now we have to find the closest perfect square of √43000. The smallest perfect square less than 43000 is 42250, and the largest perfect square more than 43000 is 43560. √43000 falls somewhere between 205 and 210.

 

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 (43000 - 42250) ÷ (43560 - 42250) = 0.75.

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 205 + 0.75 = 205.75, so the square root of 43000 is approximately 205.75.

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Common Mistakes and How to Avoid Them in the Square Root of 43000

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Square Root of 43000 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √43000?

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Explanation

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Problem 2

A square-shaped building measuring 43000 square feet is built; if each of the sides is √43000, what will be the square feet of half of the building?

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Explanation

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √43000 x 5.

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Explanation

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (43000 + 1000)?

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Explanation

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √43000 units and the width ‘w’ is 50 units.

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Explanation

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FAQ on Square Root of 43000

1.What is √43000 in its simplest form?

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2.Mention the factors of 43000.

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3.Calculate the square of 43000.

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4.Is 43000 a prime number?

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5.43000 is divisible by?

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6.How does learning Algebra help students in Thailand make better decisions in daily life?

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7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 43000?

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8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 43000?

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9.Does learning Algebra support future career opportunities for students in Thailand?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 43000

  • 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.

 

  • 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, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.

 

  • Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.

 

  • Approximation: Estimating a value based on logical reasoning and closest values, typically used to find square roots of non-perfect squares.
Professor Greenline from BrightChamps

About BrightChamps in Thailand

At BrightChamps, we understand algebra is more than just symbols—it opens up a world of opportunities! Our mission is to help children across Thailand develop essential math skills, focusing today on the Square Root of 43000 with a special look at square roots—in a lively, enjoyable, and easy-to-follow manner. Whether your child is discovering the speed of a roller coaster at Dream World, tallying local football scores, or managing their allowance to buy the latest gadgets, mastering algebra gives them confidence for everyday life. Our interactive lessons make learning fun and straightforward. Since children in Thailand have varied learning styles, we personalize our approach for each child. From Bangkok’s busy streets to Phuket’s tropical islands, BrightChamps brings math to life, making it relatable and exciting throughout Thailand. Let’s make square roots a joyful part of every child’s math journey!
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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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Max, the Girl Character from BrightChamps

Fun Fact

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

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