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Square Root

What is the square root of 18? | How to find the square 18?

Written by Prerit Jain

Updated on: 12 Aug 2023

What is the square root of 18? | How to find the square 18?

What is the square root of 18? | How to find the square 18?

The square root of 18 is 4.24264068712 mentioned with a symbol √. The square root of 18 is denoted using √18 or 181/2. In the radical form, the square root of 18 is represented as 3√2.
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 5 when multiplied by itself (5× 5) = 25. The square root for  (25) is 5. 

The square root of √18 = 1832
The square root of √18 in decimal form,
√18=  4.24264068712
The square root of √18 in exponent form, 
181/2= 4.24264068712

The calculation for the square root of 18

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 that end with 2,3,7 and 18 are not perfect square numbers.
18 is not a rational number or a perfect square number.

Prime factorization cannot be used to find the square root of 18. Hence, the long division method is used to find the square root of 18.

Methods to find 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. 

  • Step1: Find the prime factor for the given number
    √18 = 2 ×3×3
  • Step 2: Pair the prime factors.
    √18 = 2×32
    Take square on both sides
    √18=2×32
    You can cancel the square with the square root we get
    √18 = 3×√2
  • Step 3: Multiply the factors
    The √2 = 1.41421
    √18 = 3×1.41421
    √18 = 4.24264068712

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 18:

  • 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 18

  • Step 1: Find the smallest integer that can divide the number. 18 is not a perfect root number and 4 is the nearest number that can divide it. 
  • Step 2: Keep following the long division using divisor and dividend. 

Long division method

  • Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number. Hence, the √18 = 4.2426

Solved Examples

Example 1: Find the square root of 64 using the prime factorization method
Solution:
Prime factor of 64 = 2×2×2×2×2×2 or 26
Now let us take the similar squares 


Now, multiply the squares 2×2×2 = 8
Hence, the √64 = 8.
Example 2: what is the square root of 18 using the long division method
Solution:


The √18 = 4.2426
Example 3: What is the square root of 18 using repeated division
Solution:

  1. 18-1 = 17
  2. 17-3 = 14
  3. 14-5 = 9
  4.  9-7 = 2
  5. 2-9 = -7
    The last step in continuous subtraction must be zero. The square root of 18 cannot be found using repeated subtraction methods. 

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. 
Example: √2, √3, √5 or √18

Example 5: Solve √16×√18
Solution:
The √18 = 4.2426
√16 = 4
√16×√18 = 4 ×4.2426
√16×√18 = 16.970

FAQs on the square root of 18

What is the √18

The √ 18 = 4.2426

Which method is used to find the √ 18

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 18 in exponential form?

(18)1/2 or 180.5 is the exponential way to write √18

How to write the square root of √18 in radical form?

The radical form of writing square root is 18

Can I find the square root of 18 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 18 Is it an irrational number?

Yes, 18 is an irrational number since the number is not equal to zero. The square root of 18 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

Written by

Prerit Jain

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