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Last updated on May 26th, 2025

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Square Root of 1989

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If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design and finance. Here, we will discuss the square root of 1989.

Square Root of 1989 for US Students
Professor Greenline from BrightChamps

What is the Square Root of 1989?

The square root is the inverse of the square of the number. 1989 is not a perfect square. The square root of 1989 is expressed in both radical and exponential form. In the radical form, it is expressed as √1989, whereas in the exponential form, it is expressed as (1989)^(1/2). √1989 ≈ 44.5925, 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.

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Finding the Square Root of 1989

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are used. Let us now learn the following methods:

 

  • Prime factorization method
  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 1989 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 1989 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 1989

 

Breaking it down, we get 3 x 3 x 3 x 3 x 11 x 2: 3^3 x 11 x 2

 

Step 2: Now we found the prime factors of 1989. Since 1989 is not a perfect square, the digits of the number can’t be grouped in pairs.

 

Therefore, calculating √1989 using prime factorization is impractical.

Professor Greenline from BrightChamps

Square Root of 1989 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we determine 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, we group the numbers from right to left. In the case of 1989, we group it as 89 and 19.

 

Step 2: Now we need to find n whose square is closest to 19. The closest perfect square is 16 (4^2), so we choose n as 4. Now the quotient is 4.

 

Step 3: Subtract 16 from 19 to get 3, then bring down 89 to get a new dividend of 389.

 

Step 4: Double the quotient (4) to get 8, which will be part of our new divisor.

 

Step 5: We need to find a digit x such that 8x * x is less than or equal to 389. Let's try x = 4, giving 84 * 4 = 336.

 

Step 6: Subtract 336 from 389 to get 53. The quotient is now 44.

 

Step 7: Add a decimal point to the quotient and bring down two zeros to make the new dividend 5300.

 

Step 8: Double the quotient part before the decimal (44) to get 88.

 

Step 9: Find a digit y such that 88y * y is less than or equal to 5300. Let's try y = 6, giving 886 * 6 = 5316.

 

Step 10: Subtract 5316 from 5300 to get -16. Since we need to refine our guess, let's try y = 5, giving 885 * 5 = 4425.

 

Step 11: Subtract 4425 from 5300 to get 875. The quotient is now 44.5. Continue these steps until the desired precision is achieved.

 

The square root of √1989 ≈ 44.5925.

Professor Greenline from BrightChamps

Square Root of 1989 by Approximation Method

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 1989 using the approximation method.

 

Step 1: Identify the closest perfect squares to √1989. The smallest perfect square less than 1989 is 1936 (44^2) and the largest perfect square more than 1989 is 2025 (45^2). Therefore, √1989 falls between 44 and 45.

 

Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square).

 

Using the formula: (1989 - 1936) / (2025 - 1936) = 53 / 89 ≈ 0.5955 Adding this value to 44 gives us approximately 44.5955, so the square root of 1989 is approximately 44.5955.

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Common Mistakes and How to Avoid Them in the Square Root of 1989

Students may make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few common mistakes students tend to make.

Mistake 1

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Forgetting about the negative square root

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It is important to remember that a number has both positive and negative square roots. However, we typically consider only the positive square root for practical applications.

For example, √50 = 7.071, but there is also -7.071 which should not be forgotten.

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Square Root of 1989 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
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 √1989?

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The area of the square is approximately 1989 square units.

Explanation

The area of the square = side^2.

The side length is given as √1989.

Area of the square = (√1989) x (√1989) = 1989.

Therefore, the area of the square box is approximately 1989 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 1989 square feet is built; if each of the sides is √1989, what will be the square feet of half of the building?

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Approximately 994.5 square feet

Explanation

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

Dividing 1989 by 2 = approximately 994.5

So half of the building measures approximately 994.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √1989 x 5.

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Approximately 222.96

Explanation

The first step is to find the square root of 1989, which is approximately 44.5925.

The second step is to multiply 44.5925 by 5.

So, 44.5925 x 5 ≈ 222.96

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (1989 + 11)?

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The square root is approximately 45.

Explanation

To find the square root, we need to sum (1989 + 11). 1989 + 11 = 2000, and then √2000 ≈ 44.72.

Therefore, the square root of (1989 + 11) is approximately 44.72, or more precisely ±44.72 considering both positive and negative roots.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √1989 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is approximately 165.18 units.

Explanation

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

Perimeter = 2 × (√1989 + 38) Perimeter = 2 × (44.5925 + 38)

Perimeter ≈ 2 × 82.5925 ≈ 165.18 units

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FAQ on Square Root of 1989

1.What is √1989 in its simplest form?

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2.Mention the factors of 1989.

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3.Calculate the square of 1989.

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4.Is 1989 a prime number?

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5.1989 is divisible by?

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

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7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 1989?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of 1989?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 1989

  • Square root: A square root is the inverse of squaring a number. 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 expressed as a simple fraction p/q, where q is not zero and p and q are integers.
     
  • Approximation: A method used to find an estimated value that is close to the actual value, often used when dealing with irrational numbers.
     
  • Decimal: A number that contains a whole number and a fractional part separated by a decimal point, for example: 44.59.
     
  • Radical: The symbol used to denote the square root (√) or nth root of a number.
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we understand algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to empower kids throughout the United States to master key math skills, like today’s topic on the Square Root of 1989, with a special emphasis on understanding square roots—in an engaging, fun, and easy-to-grasp manner. Whether your child is calculating how fast a roller coaster zooms through Disney World, keeping track of scores during a Little League game, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence to tackle everyday problems. Our hands-on lessons make learning both accessible and exciting. Since kids in the USA learn in diverse ways, we customize our methods to suit each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps brings math alive, making it meaningful and enjoyable all across America. Let’s make square roots an exciting part of every child’s math adventure!
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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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