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Last updated on May 26th, 2025

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Square Root of 3375

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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 3375.

Square Root of 3375 for Omani Students
Professor Greenline from BrightChamps

What is the Square Root of 3375?

The square root is the inverse of the square of the number. 3375 is not a perfect square. The square root of 3375 can be expressed in both radical and exponential forms. In radical form, it is expressed as √3375, whereas in exponential form it is expressed as (3375)^(1/2). √3375 = 58.09475, 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 3375

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 3375 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 3375 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 3375 Breaking it down, we get 3 x 3 x 3 x 3 x 5 x 5 x 5: 3^4 x 5^3

 

Step 2: Now we found out the prime factors of 3375. The second step is to make pairs of those prime factors. Since 3375 is not a perfect square, the digits of the number can’t be grouped in equal pairs. Therefore, calculating 3375 using prime factorization directly is complex.

Professor Greenline from BrightChamps

Square Root of 3375 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 3375, we need to group it as 75 and 33.

 

Step 2: Now we need to find a number whose square is less than or equal to 33. We can say this number is '5' because 5 x 5 = 25, which is less than 33. After subtracting, the remainder is 8.

 

Step 3: Now let us bring down 75, making it the new dividend. Add the previous divisor with itself, 5 + 5, which results in 10, our new divisor.

 

Step 4: The new divisor will be 10n where n is such that 10n x n is less than or equal to 875. We find n = 8, as 10 x 8 x 8 = 800.

 

Step 5: Subtract 800 from 875, the remainder is 75. The quotient is now 58.

 

Step 6: Since the remainder is still present, add a decimal point and bring down two zeros, making the dividend 7500.

 

Step 7: The new divisor is 116, because 1168 x 8 = 9344, continuing this process until the desired decimal places are reached. So the square root of √3375 is approximately 58.094.

Professor Greenline from BrightChamps

Square Root of 3375 by Approximation Method

The approximation method is useful for finding square roots easily. Let us learn how to find the square root of 3375 using the approximation method.

 

Step 1: Find the closest perfect squares to √3375. The largest perfect square smaller than 3375 is 3249, and the smallest perfect square larger than 3375 is 3481. √3375 falls between 57 and 59.

 

Step 2: Apply the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square) Using the formula: (3375 - 3249) / (3481 - 3249) = 0.126 Add this decimal to the smaller estimate: 57 + 0.126 = 57.126, so the approximate square root of 3375 is 58.094.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 3375

Students often make mistakes in finding square roots, such as forgetting the negative square root, skipping steps in the long division method, etc. Let's look at a few common mistakes and how to avoid them.

Mistake 1

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Forgetting about the negative square root

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

 

For example: √50 = 7.07, but there's also -7.07.

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Square Root of 3375 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 √3375?

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

The area of the square is approximately 3375 square units.

Explanation

The area of a square = side^2.

The side length is given as √3375.

Area = (√3375) x (√3375) = 3375.

Therefore, the area of the square box is 3375 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 3375 square feet is built; if each of the sides is √3375, what will be the square feet of half of the building?

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1687.5 square feet

Explanation

Divide the given area by 2 as the building is square-shaped. Dividing 3375 by 2 gives 1687.5. So half of the building measures 1687.5 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √3375 x 5.

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Approximately 290.47

Explanation

First, find the square root of 3375, which is approximately 58.094. Then, multiply 58.094 by 5. So, 58.094 x 5 = approximately 290.47.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (3375 + 25)?

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The square root is approximately 59.16

Explanation

To find the square root, first find the sum: 3375 + 25 = 3400. Then, calculate √3400, which is approximately 58.30952.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √3375 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 216.188 units.

Explanation

Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3375 + 50) = 2 × (58.094 + 50) = 2 × 108.094 = approximately 216.188 units.

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FAQ on Square Root of 3375

1.What is √3375 in its simplest form?

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2.Mention the factors of 3375.

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3.Calculate the square of 3375.

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4.Is 3375 a prime number?

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5.3375 is divisible by?

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

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7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 3375?

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8.How do technology and digital tools in Oman support learning Algebra and Square Root of 3375?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 3375

  • 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, so √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 often more relevant in practical applications, which is why it is also known as the principal square root.

 

  • Prime factorization: Breaking down a number into its basic building blocks, specifically prime numbers. For example, the prime factorization of 3375 is 3^4 x 5^3.

 

  • Long division method: A technique used to find the square root of a non-perfect square by dividing the number into groups and using a systematic approach to approximate the square root.
Professor Greenline from BrightChamps

About BrightChamps in Oman

At BrightChamps, we understand algebra as more than symbols—it’s a key to unlocking many opportunities! Our mission is to help children across Oman gain important math skills, focusing today on the Square Root of 3375 with special attention to square roots—in an engaging, lively, and easy-to-follow manner. Whether your child is measuring how fast a roller coaster moves at Oman’s Dreamland Aqua Park, tracking local football scores, or managing their allowance for the latest gadgets, mastering algebra gives them confidence for everyday tasks. Our hands-on lessons make learning simple and fun. Because children in Oman learn differently, we adapt lessons to fit each learner’s style. From Muscat’s vibrant city life to beautiful natural landscapes, BrightChamps brings math to life, making it exciting throughout Oman. 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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