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Square Root

What is the square root of 27? How to find the square root of 27?

Written by Prerit Jain

Updated on: 12 Aug 2023

What is the square root of 27? How to find the square root of 27?

What is the square root of 27? How to find the square root of 27?

The square root of 27 is 5.1961. The square root of 27 is denoted using √27 or 271/2. In the radical form, the square root of 27 is represented as 3√3.
The square root of a number is determined when a quantity of a number is produced when multiplied by itself or a factor of a number when multiplied by itself gives the original number.

In simple terms, when a value is multiplied by itself it gives the original number. For a better understanding,
the number 15 when multiplied by itself (15×15) = 225. The square root for  (√225) is 15. 
Square root of  √27 = √27±3√3
The square root of 27 in decimal form,
√27=  5.1961
The square root of 27 in exponent form, 
271/2= 5.1961

What is the square root of 27?

The square root of a number when multiplied itself gives the original number. The square root of 27 is expressed as √27
√27 = √(Number) × √(Number)
√27 = (5.1961×5.1961)
√27 = √(5.1961)2
Now, remove the square on the right-hand side we get.
√27 = 5.1961
Thus, by multiplying 5.1961 we get the number 27.

The square root of 27 in radical form

The number 27 is a perfect cube number and hence can be expressed in radical form.
√27 = √3×√3×√3
√27 = 3×√32
√27 = 3√3

The calculation for the square root of 27

To find the square root of any number first the given number is usually checked to determine whether they are a perfect square number or not. The square root of the number is found using the long division method.

For the numbers with a perfect square, it is easy to find the square roots and it is a bit tough for non-square values. Numbers like 4,9, 16,25, etc., are perfect squares. Numbers such as 2,3,7 and 18 are not perfect square numbers.
27 is not a rational number or a perfect square number.

Prime factorization cannot be used to find the square root of  27. Hence, the long division method is used to find the square root of 27.

Methods to find the square root

There are three methods to find the square root of a number

  • Prime factorization method
  • Long division method
  • Repeated subtraction

These methods described above do not apply to finding the square root of any number.  

Prime factorization method

To find the square root of a number using the prime factorization method first knows the prime factors of the numbers. Let us take n as a prime number, by grouping their squares we get n2 now multiplying them we get the square root of the number. 

  • Step 1: Find the prime factor for the given number
    √27 = 3×3×3
  • Step 2: Pair the prime factors
    √27 = 3×32
    Take square on both sides
    √27=√3×√32
    You can cancel the square with the square root we get
    √27 = 3√3
  • Step 3: Multiply the factors
    The √3 = 1.732
    √27 = 3×1.732
    √27 = 5.196

Long division method

Long division is one of the easiest methods to find the square root of any number. It was the preferred method to be used for the non-perfect square numbers. Find the integer that can divide the number and proceed with the long division. 

Steps to find the square root of 27:

  • Step 1: Find the smallest integer that can divide the number. 
  • Step 2: Keep following the long division using divisor and dividend. 
  • Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.  

Find the square root of 27

  • Step 1: Find the smallest integer that can divide the number. 27 is not a perfect root number and 5 is the nearest number that can divide it. 
  • Step 2: Keep following the long division using divisor and dividend. 
Long division method for the square root of 27
  • Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number. Hence, the √ 27 = 5.1961

Solved Examples

Example 1: Find the square root of 225 using the prime factorization method
Solution:
Prime factor of 225 = 3×3×5×5
Now, multiply the squares 3×5 = 15
Hence, the square root of 225 is
√225 = 15.

Example 2: What is the square root of 27 using the long division method?
Solution:

The √27 = 5.1961

Example 3: Solve (√3×√27)+9
Solution:
The number 27 is a perfect cube number and can be written as 3√3
(√3×√27)+9 = (3√3×√3)+9
(√3×√27)+9 = 3×3+9
(√3×√27)+9 = 9+9
(√3×√27)+9 = 18.

Example 4: What is an irrational number?
Solution:
 A number is said to be an irrational number if it cannot be expressed in the form of a ratio or fractions. 
Examples of irrational numbers √2, √3, √5, or √27.

Example 5: Solve 16√27
Solution:
The √27 = 5.1961
16√27 = 16×5.1961
16√27 = 83.1376

FAQs on the square root of 27

What is the √27?

The 27 = 5.1961

Which method is used to find the 27?

The standard method that is used to find the square root of any number is the long division method.

How to write the square root of 27 in exponential form? 

(27)1/2 or 270.5 is the exponential way to write 27.

How to write the square root of 27 in radical form?

The radical form of writing square root is 33

Can I find the square root of 27 using other methods?

Apart from the long division method, prime factorization and repeated subtraction are two methods that are used to find the square root of the number. Repeated subtraction is not applicable to irrational numbers.

Is 27 Is it an irrational number?

Yes, 27 is an irrational number since the number is not equal to zero. The square root of 27 cannot be expressed in ratios or fractions. 

What are the methods to find the square root of a number?

There are three methods to find the square root of a number
Prime factorization method
Long division method
Repeated subtraction

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Prerit Jain

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