Square Root of 18

The square root of 18 is ±4.24264068712, where is 4.24264068712 the positive solution of the equation x² = 18.

Finding the square root is just the inverse of squaring a number and hence, squaring 4.24264068712 will result in 18.

The square root of 18 is written as √18 in radical form, where the ‘√’  sign is called the “radical”  sign. In exponential form, it is written as (18)^1/2 
 

We can find the square root of 18 through various methods. They are:

• Prime factorization method

• Long division method

•  Approximation/Estimation method
   

The prime factorization of 18 is done by dividing 18 by prime numbers and continuing to divide the quotients until they can’t be separated anymore.

After factorizing 18, make pairs out of the factors to get the square root. If there exist numbers that cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs

So, Prime factorization of 18 = 3 × 3 × 2   

But here in the case of 18, a pair of factor 3 can be obtained but a single 2 is remaining

So, it can be expressed as  √18 =   √(3 × 3 × 2) = 3√2

 3√2 is the simplest radical form of √18

This method is used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 18:

 Step 1: Write the number 18, and draw a bar above the pair of digits from right to left.
               
Step 2: Now, find the greatest number whose square is less than or equal to. Here, it is 4, Because 4²=16 < 18.

Step 3 : Now divide 18 by 4 (the number we got from Step 2) such that we get 4 as quotient and we get a remainder.Double the divisor 4, we get 8, and then the largest possible number A1=2 is chosen such that when 2 is written beside the new divisor, 8, a 2-digit number is formed →82, and multiplying 2 with 82 gives 164 which is less than 200.

Repeat the process until you reach the remainder of 0.

We are left with the remainder, 34524 (refer to the picture), after some iteration  and keeping the division till here, at this point 
             
Step 4 : The quotient obtained is the square root. In this case, it is 4.2426….

Approximation or estimation of the square root is not the exact square root, but it is an estimate. Here, through this method, an approximate value of square root is found by guessing.

Follow the steps below:

Step 1:  identify the square roots of the perfect squares above and below 18

             Below : 16→ square root of 16 = 4     ……..(i)
             Above : 25 →square root of 25 = 5     ……..(ii)

Step 2: Dividing 18 with one of 4 or 5. If we choose 4 

            We get 4.5 when 18 is divided by 4    …….(iii)

             
Step 3:  find the average of 4 (from (i)) and 4.5 (from (iii))

            (4+4.5)/2 = 4.25 

            
 Hence, 4.25 is the approximate square root of 18
 

• Exponential form:  An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 × 2 × 2 × 2 = 16 Or, 2 4 = 16, where 2 is the base, 4 is the exponent 

• Prime Factorization:  Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3

• Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....

• Rational numbers and Irrational numbers: The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 

• Perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24