Square Root of 196

Square root of 196 is 14 and is represented as √196 = ±14. Observe the expression “±a × ±a = s”. Here ‘s’ is termed as the perfect square number as it is multiplied by an integer “a” with itself. “a” will be termed as the perfect square root. Since “a” is an integer, it can be either positive or negative. However the perfect square will always be positive. Similarly 196 can be obtained by multiplying ±14 with ±14. Hence 196 is a perfect square and ±14, a perfect square root. The method of obtaining the square root is by using the prime factorisation method, long division method, simplified method and repeated subtraction method. Squares and Square roots can help you understand more about roots and squares. 

Note the Following:

The Square root of 196 = √196 where ‘√’ = radical, and 196 is the radicand.

Exponential Form of Square root of 196 = 196^1/2

Solution for √196 = 14

Square root of 196 is Irrational = False

What is the Square root of 196?

The square root of 196 is 14. In other words, the square of 14 is 196. i.e ±14 × ±14 is 196. 

How to Find the Square root of 196?

There are three methods to find the Square root of 196:

• Prime Factorisation method
• Long Division method
• Repeated Subtraction method

Square root of 196 by Prime Factorisation Method

In the Prime Factorisation method, the steps are

1. Divide 196 by prime divisors, starting by 2.
2. Group the same two prime numbers and remove 1 from the root ( 2, 2 and 7, 7 forms the group).
3. Product of the number outside the root ( 2 × 7) forms the square root of 196.

Above steps for 196 will be expressed as:

196 = 2 × 2 × 2 × 7

196 = (2 × 2) × (7 × 7) 

√196 = √((2 × 2) × (7 × 7)) 

√196 = 2 × 7

√196 = 14

Therefore the square root of 196 = 14.

Square root of 196 by Long Division Method

In the long division method, the given numbers are paired in groups, starting from the right side. Let us understand the long division method, in detailed steps;

Step 1:  Grouping the given number into pairs

Given number is 196, grouping it as 2 and 56.

Step 2: Consider the first number.

Let us find a square number that divides the first number

i.e 1 × 1 = 1 

2 × 2 = 4 

3 × 3 = 9.

Step 3: Continue the division using the next number 96. The first number to be used as the next divisor (Divisor of first division multiplied by quotient of first division)

No more division is possible as the remainder is zero. Hence the quotient is the square root of the given number. 

Therefore the Square root of 196 is 14.

Square root of 196 by Repeated Subtraction Method.

In the repeated subtraction method, the number 196 is subtracted repeatedly by odd numbers. There are two possibilities.

1. Difference = zero, 196 is a perfect square and the step number is the square root of 196.
2. Difference = negative, 196 is not a perfect square and it does not have a rational root. 

For the given number 196, steps for repeated subtraction are

In the repeated subtraction the Step 14 becomes zero, which implies that 196 is a perfect square number and hence 14 is its root. 

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Solved Examples

1. Find the square root of 196 by pairing factors.

The pairs of 196 are (1, 196), (2, 98), (4, 49), (7, 28) and (14, 14)

Therefore, the square root of 196 is 14 using pairing factors 14 and 14. 

1. What is the square of 14?

The square of 14 is nothing but 14 times 14 and that is 196.