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Last updated on May 26th, 2025

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Square Root of 3125

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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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 3125.

Square Root of 3125 for US Students
Professor Greenline from BrightChamps

What is the Square Root of 3125?

The square root is the inverse of the square of the number. 3125 is not a perfect square. The square root of 3125 is expressed in both radical and exponential form. In the radical form, it is expressed as √3125, whereas (3125)^(1/2) in the exponential form. √3125 ≈ 55.9017, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 3125

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
Professor Greenline from BrightChamps

Square Root of 3125 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 3125 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 3125 Breaking it down, we get 5 x 5 x 5 x 5 x 5: 5^5

 

Step 2: Now we found out the prime factors of 3125. The second step is to make pairs of those prime factors. Since 3125 is not a perfect square, the digits of the number can’t be grouped entirely in pairs. Therefore, calculating the square root of 3125 using prime factorization involves simplifying it to √(5^2 × 5^2 × 5) = 25√5.

Professor Greenline from BrightChamps

Square Root of 3125 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 3125, we need to group it as 31 and 25.

 

Step 2: Now we need to find n whose square is less than or equal to 31. We can say n is '5' because 5^2 = 25 is less than 31. Now the quotient is 5, after subtracting 31-25, the remainder is 6.

 

Step 3: Now let us bring down 25, making the new dividend 625. Add the old divisor (5) with the same number to get 10, which will be our new divisor (5 becomes 50 when we double it as part of the calculation).

 

Step 4: The new divisor will be 10n; we need to find the value of n such that 10n x n ≤ 625. Choosing n as 5 works because 105 x 5 = 525.

 

Step 5: Subtract 525 from 625; the difference is 100, and the quotient is 55.

 

Step 6: Since the new dividend (100) is less than the new divisor (105), 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 10000.

 

Step 7: Now we need to find the new divisor, which will be 110n, where n = 9. Because 1109 ✖ 9 = 9981, which is close to 10000.

 

Step 8: Subtracting 9981 from 10000 gives us 19.

 

Step 9: Continue doing these steps until we achieve sufficient precision. So the square root of √3125 is approximately 55.9017.

Professor Greenline from BrightChamps

Square Root of 3125 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 3125 using the approximation method.

 

Step 1: We need to find the closest perfect squares of √3125. The smallest perfect square below 3125 is 3025 (which is 55^2), and the largest perfect square above 3125 is 3136 (which is 56^2). √3125 falls somewhere between 55 and 56.

 

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (3125 - 3025) / (3136 - 3025) = 100 / 111 ≈ 0.9009. Adding this value to the integer part gives us approximately 55.9009. Therefore, the square root of 3125 is approximately 55.9017.

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Common Mistakes and How to Avoid Them in the Square Root of 3125

Students do make mistakes while finding square roots, such as forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes in detail.

Mistake 1

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Forgetting about the negative square root

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It is important for students to understand that a number has both positive and negative square roots. However, we usually consider only the positive square root, as it is the most relevant in real-world applications.

 

For example: √3125 ≈ 55.9017, but there is also -55.9017, which should not be ignored in some contexts.

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Square Root of 3125 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 √3125?

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The area of the square is 3125 square units.

Explanation

The area of the square = side^2.

The side length is given as √3125.

Area of the square = side^2 = √3125 × √3125 = 3125.

Therefore, the area of the square box is 3125 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped field measuring 3125 square feet is built; if each of the sides is √3125, what will be the square feet of half of the field?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

1562.5 square feet

Explanation

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

Dividing 3125 by 2 = we get 1562.5.

So half of the field measures 1562.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √3125 × 3.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

167.7051

Explanation

The first step is to find the square root of 3125, which is approximately 55.9017.

The second step is to multiply 55.9017 by 3.

So 55.9017 × 3 ≈ 167.7051.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (3125 + 25)?

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The square root is approximately 56.7005.

Explanation

To find the square root, we need to find the sum of (3125 + 25). 3125 + 25 = 3150, and then √3150 ≈ 56.7005.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length 'l' is √3125 units and the width 'w' is 50 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The perimeter of the rectangle is approximately 211.8034 units.

Explanation

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

Perimeter = 2 × (√3125 + 50) ≈ 2 × (55.9017 + 50) ≈ 2 × 105.9017 ≈ 211.8034 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 3125

1.What is √3125 in its simplest form?

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2.Mention the factors of 3125.

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3.Calculate the square of 3125.

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4.Is 3125 a prime number?

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5.3125 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 3125?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of 3125?

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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 3125

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse is the square root, √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, but the positive square root is usually more relevant in real-world applications.

 

  • Prime factorization: Breaking down a number into its basic prime number components. For example, the prime factorization of 3125 is 5^5.

 

  • Long division method: A technique for finding square roots of numbers that are not perfect squares by dividing and averaging.
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 3125, 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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