Square root of 196
The square root of any number is a number when multiplied with itself results in the given number. The square root of a number can be a real number or imaginary number. The square root of 196 is the number whose product with itself gives 196. In this minilesson, we will find the square root of 196 by prime factorization method and long division method along with few interesting problems.
 Square root of 196: √196 = 14
 Square of 196: 196² = 38416
1.  What Is the Square Root of 196? 
2.  Is Square Root of 196 Rational or Irrational? 
3.  How to Find the Square Root of 196? 
4.  FAQs on Square Root of 196 
What is The Square Root of 196?
 Square root of 196 is expressed as √196 in radical form.
 Square root of 196 = √196 = √(14 × 14) = +14 and 14
 Square root of 196 is represented as (196)^{1/2} in exponential form.
Is Square Root of 196 Rational or Irrational?
 The square roots of 196 are +14 and 14
 Both +14 and 14 can be represented in the form of p/q, that is +14/1 and 14/1
 A number is called a rational number when it can be represented in the form of p/q where q ≠
 Therefore, the square root of 196 is a rational number.
How to Find The Square Root of 196?
Let’s calculate the square root of 196 by prime factorization or long division method.
Square Root of 196 By Prime Factorization Method
 Prime factorization of 196: 2^{2} × 7^{2}
 Prime factors of 196 in pairs: (2 × 2) × (7 × 7)
 Now square root of 196: √196 = √(2 × 2) × (7 × 7)
√196 = √(2 × 7)^{2}
√196 = (2 × 7) = 14
So, the square root of 196 is 14.
Square Root of 196 By Long Division
With the help of the following steps, we can find the square root of 196 by the long division method.
Step1. Write 196 as shown in the figure. Start pairing the digits from the right end in pairs of two by putting a bar on top of them. So, we got two pairs of 1 and 96
Step2. Now find a number (n) such that n × n is a number less than equal to 1. Hence, n = 1.
Step3. Now subtract the obtained value from the first pair in the dividend and add the divisor with itself (n + n). Now bring the second pair down (96).
Step4. Now find a number (m) such that 2m × m is less than equal to 96. Here m will be 4 as 24 × 4 = 96.
So, we get the square root of √196 = 14 by the long division method.
Explore square roots using illustrations and interactive examples
Challenging Questions:
 Find the square root of the first three multiples of 196?
 Find the square root of 196?
Important Notes:
 Both +14 and 14 are square roots of 196
 There will be n/2 digits in the square root of an even number with n digits.
 There will be (n+2)/2 digits in the square root of an odd number with n digits.
 196 is a perfect square.
Square Root of 196 Solved Examples

Example 1: Eric wants to find out how many factors of 196 are perfect squares?
Solution:
Factors of 196: 1, 2, 4, 7, 14, 28, 49, 56, 98, 196
Now among the following numbers 1, 4, 49, and 196 are perfect square
So, 4 factors of 196 are perfect squares which are 1, 4, 49, and 196. 
Example 2: Xavi is curating a squareshaped field with an area of 196 square feet. He wants the final length of one side 12 feet, by how much he should reduce the length of one side?
Solution:
Area of the field = (Length of side)^{2} = 196 sqft.
Length of side = Square root of 196 = √196 = 14 ft
The final required length of one side = 12 ft
Therefore length of side is reduced by = 14 – 12 = 2 ft. 
Example 3: Sean wants to find out the square root of 196 using the repeated subtraction method. Can you assist Sean?
Solution:
196  1 = 195
195  3 = 192
192  5 = 187
187  7 = 180
180  9 = 171
171  11 = 160
160  13 = 147
147  15 = 132
132  17 = 115
115  19 = 96
96  21 = 75
75  23 = 0
52  25 = 27
27  27 = 0
As we have subtracted 14 times to get zero
Therefore, the square root of 196 is 14.
FAQs on Square Roots of 196
Is 14 a square root of 196?
Yes 14 is a square root of 196
Because 14 × 14 = 196
Is the number 196 a perfect square?
A perfect square is a number whose factors are square of a number
As the factors of 196 are square of 2 and 7, 2² × 7².
Hence, 196 is a perfect square.
What are the prime factors of 196 and the prime factorization of 196?
Prime factors of 196 are 2 and 7
Prime factorization of 196: 2² × 7²
Are the square roots of 196 rational?
The square roots of 196 are +14 and 14
Both +14 and 14 can be represented in the form of p/q. So, the roots of 196 are rational.
Can we find the square root of 196 by the approximation method?
No, we cannot estimate the square root of 196 using the approximation method
This method can only be used if the given number lies between two consecutive perfect squares.