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Last updated on May 26th, 2025

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Square Root of 27/4

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If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The square root is used in various fields like vehicle design, finance, etc. Here, we will discuss the square root of 27/4.

Square Root of 27/4 for Omani Students
Professor Greenline from BrightChamps

What is the Square Root of 27/4?

The square root is the inverse of the square of the number. 27/4 is not a perfect square. The square root of 27/4 is expressed in both radical and exponential form. In the radical form, it is expressed as √(27/4), whereas in the exponential form it is expressed as (27/4)^(1/2). √(27/4) = √27/2 = 2.59808, 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 27/4

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 27/4, the long-division and approximation methods are used. Let us now learn the following methods:

 

  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 27/4 by Long Division Method

The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root of 27/4 using the long division method, step by step.

 

Step 1: First, express the number as a decimal. 27/4 = 6.75.

 

Step 2: Group the digits from right to left as 6.75.

 

Step 3: Find n whose square is closest to 6. The closest is 2, because 2² = 4.

 

Step 4: Subtract 4 from 6, bringing down 75 to get 275.

 

Step 5: Double the quotient obtained, which is 2, to get 4 and find a digit x such that 4x × x ≤ 275. The suitable x is 5, as 45 × 5 = 225.

 

Step 6: Subtract 225 from 275 to get 50.

 

Step 7: Add a decimal point and bring down 00 to make it 5000.

 

Step 8: Double the quotient 25 to get 50, then find x such that 50x × x ≤ 5000. The suitable x is 9, as 509 × 9 = 4581.

 

Step 9: Subtract 4581 from 5000 to get 419.

 

Step 10: Continue this process to get more decimal places.

 

The square root of 6.75 is approximately 2.59808.

Professor Greenline from BrightChamps

Square Root of 27/4 by Approximation Method

The approximation method is another method for finding square roots. Let us learn how to find the square root of 27/4 using the approximation method.

 

Step 1: Find the closest perfect squares around 27/4. The smallest perfect square is 4 and the largest perfect square is 9. √(27/4) lies between √4 = 2 and √9 = 3.

 

Step 2: Apply the formula (Given number - smallest perfect square)/(Greater perfect square - smallest perfect square). Using the formula, (6.75 - 4)/(9 - 4) = 0.55.

 

Step 3: Add this decimal to the smaller root: 2 + 0.55 = 2.55. Adjust further by checking higher precision to approximate further.

 

Thus, the square root of 6.75 is approximately 2.59808.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 27/4

Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division methods. 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 to remember that a number has both positive and negative square roots. However, we commonly use only the positive square root.

For example, √50 = 7.07, but there is also -7.07, which should not be forgotten.

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Square root of 27/4 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 √(27/4)?

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The area of the square is approximately 6.75 square units.

Explanation

The area of the square = side².

The side length is given as √(27/4) = 2.59808.

Area of the square = (2.59808)²

≈ 6.75.

Therefore, the area of the square box is approximately 6.75 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 27/4 square feet is built; if each of the sides is √(27/4), what will be the square feet of half of the building?

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

3.375 square feet

Explanation

Divide the given area by 2 as the building is square-shaped.

Dividing 27/4 by 2 gives 3.375.

So half of the building measures 3.375 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(27/4) × 5.

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12.9904

Explanation

First, find the square root of 27/4, which is approximately 2.59808. Then multiply 2.59808 by 5. So, 2.59808 × 5 ≈ 12.9904.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (27/4 + 5)?

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The square root is approximately 3.5.

Explanation

Find the sum of (27/4 + 5) = 6.75 + 5 = 11.75.

Then find the square root of 11.75, which is approximately 3.5.

Therefore, the square root of (27/4 + 5) is approximately ±3.5.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length 'l' is √(27/4) units and the width 'w' is 5 units.

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The perimeter of the rectangle is approximately 15.19616 units.

Explanation

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

Perimeter = 2 × (√(27/4) + 5)

≈ 2 × (2.59808 + 5)

≈ 2 × 7.59808

≈ 15.19616 units.

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

FAQ on Square Root of 27/4

1.What is √(27/4) in its simplest form?

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2.Mention the factors of 27/4.

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3.Calculate the square of 27/4.

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4.Is 27/4 a prime number?

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5.27/4 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 27/4?

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8.How do technology and digital tools in Oman support learning Algebra and Square Root of 27/4?

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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 27/4

  • Square root: A square root is the inverse operation of squaring a number. Example: 4² = 16 and the inverse is √16 = 4.
     
  • Irrational number: An irrational number cannot be expressed as a simple fraction. Its decimal form is non-repeating and non-terminating.
     
  • Decimal: A number that has a whole part and a fractional part separated by a decimal point, e.g., 7.86, 8.65.
     
  • Exponent: An exponent refers to the number of times a number is multiplied by itself. Example: 2³ = 2 × 2 × 2 = 8.
     
  • Fraction: A fraction represents a part of a whole or a division of quantities, expressed as a numerator/denominator, e.g., 3/4.
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 27/4 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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