The number 194 is a number with only two prime factors 2 and 97. So, the square root of 194 cannot be simplified further using the prime factorization method. The square root of (N) implies a number whose product with itself gives us the number N. We will now find the value of the square root of 194 using various methods and will also solve some interesting problems for better understanding.

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Square root of 194: √194 = 13.9283Square of 194: (194)2 = 37636
 1 What Is the Square Root of 194? 2 Is Square Root of 194 Rational or Irrational? 3 How to Find the Square Root of 194? 4 Important Notes on Square Root of 194 5 FAQs on Square Root of 194

## What is the Square Root of 194?

The square root of 194 in decimal form is 13.9283.The square root of 194 can be written as (194)1/2 in exponential form.The square root of 194 is written as √194 in radical form.

## Is Square Root of 194 Rational or Irrational?

The square root of 194 is a non-repeating and non-terminating number.And a rational number is a number that can be expressed in the form of p/q where q ≠ 0.Hence, the square root of 194 is an irrational number.

## How to Find the Square Root of 194?

We will now find the square root of 194 using the below-given methods

### Square Root of 194 Using Approximation Method

Firstly, find two consecutive perfect squares such that 194 lies between them. The two perfect squares are 169 (132) and 196 (142).So, the whole number part of the square root of 194 will be 13.Now, for the decimal part we will use the formula:(Given number - Smaller perfect square) / (Greater perfect square - smaller perfect square)= (194 - 169)/(196 - 169) = 25/27 = 0.926Hence, the approx. the square root of 194 by the approximation method is 13.926

### Square Root of 194 By Long Division

Now we will calculate the square root of 194 by the long division method.

Start pairing the digits by adding a bar on top of them from the unit’s place in pairs of two. We will have two pairs in this case (1 & 94).Find a number(a) such that a × a ≤ 1. So, a will be 1 as 1 × 1 = 1.Now, find a number(y) such that 2y × y ≤ 94. The number y will be 3 as 23 × 3 = 69 ≤ 94.Put a decimal in the dividend and quotient simultaneously. Also, place 3 pairs of zero in the dividend part after the decimal and repeat the above step for the three pairs of zero.

So, we get the square root of √194 = 13.928 by the long division method.

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Important Notes:

The square root of 194 is an irrational number.The square root of -194 is an imaginary number.The number 194 is not a perfect square.