Square Root of 27/4
2026-02-28 06:01 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-27/4

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Last updated on August 5, 2025

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.

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.

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

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.

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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.

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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(27/4)?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets 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.

Well explained 👍

Problem 3

Calculate √(27/4) × 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

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

Okay, lets begin

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.

Well explained 👍

Problem 5

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

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 27/4

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

The square root of 27/4 in its simplest form is √27/2, as 27 does not have a perfect square factor other than 1.

2.Mention the factors of 27/4.

Factors of 27/4 are not typically discussed, as it is a fraction, but the factors of the numerator (27) are 1, 3, 9, and 27, and the denominator (4) are 1, 2, and 4.

3.Calculate the square of 27/4.

We get the square of 27/4 by multiplying the number by itself, which is (27/4) × (27/4) = 729/16 = 45.5625.

4.Is 27/4 a prime number?

27/4 is not a prime number, as it is a fraction, and prime numbers are defined only for integers.

5.27/4 is divisible by?

As a fraction, 27/4 is not divisible in the conventional sense. However, 27 is divisible by 1, 3, 9, and 27, while 4 is divisible by 1, 2, and 4.

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.

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