Square root of 200

The square root of 200 is ±14.1421356237.

The positive value, 14.1421356237 is the solution of the equation x² = 200. As defined, the square root is just the inverse of squaring a number, so, squaring 14.1421356237 will result in 200.  The square root of 200 is expressed as √200 in radical form, where the ‘√’  sign is called “radical”  sign. In exponential form, it is written as (200)^1/2  
 

We can find the square root of 200 through various methods. They are:

• Prime factorization method

• Long division method

• Approximation/Estimation method

The prime factorization of 200 involves breaking down a number into its factors. Divide 200 by prime numbers, and continue to divide the quotients until they can’t be separated anymore.

After factorizing 200, make pairs out of the factors to get the square root. If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs

So, Prime factorization of 200 = 2  ×2 ×2 ×5 ×5  

  
for 200, two pairs of factors 2 and of factor 5 are obtained, but a single 2 is remaining.

So, it can be expressed as  √200 = √(2 ×2 ×2 × 5 ×5) = 10√2

10√2 is the simplest radical form of √200

This is a method 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 200:

Step 1 : Write the number 200, 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 2. Here, it is 1, Because 1²=1 ≤1 

Step 3 : Now divide 200 by 1 (the number we got from Step 2) such that we get 1 as quotient, and we get a remainder. Double the divisor 1, we get 2 and then the largest possible number A1=4 is chosen such that when 4 is written beside the new divisor, 2, a 2-digit number is formed →24 and multiplying 4 with 24 gives 96 which is less than 100.

Repeat the process until you reach remainder 0

We are left with the remainder, 3836 (refer to the picture), after some iterations and keeping the division till here, at this point 

             
Step 4 : The quotient obtained is the square root. In this case, it is 14.142…

Approximation or estimation of 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 200

Below : 196→ square root of 196 = 14     ……..(i)

 Above : 225 →square root of 225= 15     ……..(ii)

Step 2 : Divide 200 with one of 14 or 15

 If we choose 14, and divide 200 by 14, we get 14.2857   …….(iii)

             
Step 3: Find the average of 14 (from (i)) and 14.2857 (from (iii))

(14+14.2857)/2 = 14.14285…

            
 Hence, 14.1428 is the approximate square root of 200
 

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, 2⁴ = 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