What is the square root of 196? How to find the square root of 196?

The square root of 196 is 14. The square root of any number is just the inversion of squaring the given number. The number when multiplied twice gives the original value.

For the given number 196, when the number 14 is squared 14² or when multiplied twice by 14×14 we get 196. For a perfect square number like 196 finding the square root of the number is simple as they are whole numbers and not integers.

Long division is used to find the square root of irrational and non-perfect square numbers. Since 196 can be the ratio of two numbers it is a rational number
p/q, q = 0.

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Methods to find the square root of a number

There are three methods that are used to find the square root of a number that has perfect squares,

• Long division method
• Repeated subtraction method
• Prime factorization method

Long division method

• Step 1: Find the smallest integer that can divide the number. 
  196 is not a perfect root number and 14 is the nearest number that can divide it. 
• 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.
Hence, √196 = 14.

Repeated subtraction method

Using the repeated subtraction method, the square root of the number can be easily solved but consumes time. Hence, the prime factorization and the long division method are widely used to find the square root of the number.

Start subtracting the given number by the first odd number, take the given value, and further subtract the number with the next odd number repeat the step until you reach zero. 

Step 1	196-1	195
Step 2	195-3	192
Step 3	192-5	187
Step 4	187-7	180
Step 5	180-9	171
Step 6	171-11	160
Step 7	160-13	147
Step 8	147-15	132
Step 9	132-17	115
Step 10	115-19	96
Step 11	96-21	75
Step 12	75-23	52
Step 13	52-25	27
Step 14	27-27	0

In step 14 the number zero is obtained.
Hence √196 = 14.

Prime factorization method

Prime factorization is one of the simplest methods used to find the square root of a given number. Take the prime factor of the number as n square the given number we get n², take a single value, and multiply with the other square. By doing so we will get the square root of the number.

• Step 1: Find the prime factor for the given number
  196 = 2×2×7×7
• Step 2: Pair the prime factors.
  196 = (2×2)(7×7)
  Take square on both sides
  √196=√2×√2×√7×√7
  You can cancel the square with the square root we get
  √196 = 2×2×7×7
• Step 3: Multiply the factors
  The √196 = 2×7
  √196 = 14

Solved Examples

Example 1: What is the sum of the square of 196 and the square root of 196?
Solution:
Square of 196= 38,416
The square root of 196 = 14
The sum of the square of 196 and the square root of 196 = 38,416+14 = 38,430

Example 2: John wants to find the square root value of 64/196 to help him solve the sum.
Solution:
The √196 = 14.
The √64 = 8
Therefore, √64/196 = 8/14 = 4/7.

Example 3: Solve √196 + 2 √196
Solution:
The √196 = 14.
Hence 14 + 2 (14).
= 14+28
=42.

Example 4: what is the area of the square whose each side is equal to 14 cm
Solution:
Area of the square = x²
Here x= 14
Therefore, 14² = 14×14 = 196
Hence the area of the square with 14 cm = 196 sq. cm.

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FAQs on the square root of 196