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Square Root

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

Written by Prerit Jain

Updated on: 12 Aug 2023

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

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.

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. 
Long division method for the square root of 196

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 1196-1195
Step 2195-3192
Step 3192-5187
Step 4187-7180
Step 5180-9171
Step 6171-11160
Step 7160-13147
Step 8147-15132
Step 9132-17115
Step 10115-1996
Step 1196-2175
Step 1275-2352
Step 1352-2527
Step 1427-270
Repeated subtraction of square root 196

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.

FAQs on the square root of 196

What is the square root of 196?

The square root of 196 = 14.

Explain why the square root of 196 is a rational number

When finding the prime factor of 196 we get 142 which is entirely an even power and hence all the numbers are positive integers which makes them rational numbers.

What is the value of 196 and the square root of 196?

The square root of 196 is 14, therefore √196×196 = 196×14 = 2744

What is the real value for the square root of 196?

The actual value for the √196 = 14

What is the square root of 5?

The square root of 5 = 2.23

What is the square root of (-196)?

The square root of minus digits is imaginary numbers or imaginary units which really don’t have a square root.

Is 196 a perfect square number?

Yes, 196 is a perfect square number.

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Prerit Jain

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