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 mini-lesson, 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

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.

• 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.

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: 2² × 7²
• 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

• Square root of 22
• Square root of 169
• Square root of 14
• Square root of 68
• Square root of 17

• Find the square root of the first three multiples of 196?
• Find the square root of -196?

• 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.

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.