Square Root of 194
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.
 Square root of 194: √194 = 13.9283
 Square 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.
 The number 194 only has two prime factors that are, 2 and 97. Hence, its square root cannot be simplified further using the prime factorization.
Is Square Root of 194 Rational or Irrational?
The square root of 194 is a nonrepeating and nonterminating 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 belowgiven 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 (13^{2}) and 196 (14^{2}).
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 = 0.926  Hence, 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.
 We get the quotient as 1. Now, we will add the divisor a with itself and get the new divisor (2). Bring down the next pair (94). So, the dividend becomes 094.
 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.
Explore square roots using illustrations and interactive examples
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.
Square Root of 194 Solved Examples

Example 1: Gordon wants to know the %error in the square root of 194 calculated by the approximation method and whether it is over or underestimated. Can you help Gordon?
Solution:
The value of the square root of 194 is √194 = 13.928
The value of the square root of 194 calculated by approximation method is V194 = 13.926
As the value is less than the actual value so, it is underestimated
Now %error = ((13.928 – 13.926)/13.928) × 100 = 0.014% 
Example 2: What number should be multiplied to 194 to make it a perfect square 196?
Solution:
Square root of 194 lies between 13 and 14.
To make it a perfect square number 196,
y × 194 = 196
y = 196 / 194 = 1.0103
y = 1.0103
The number is 1.0103.
On multiplying 1.0103 by 194 we get resultant as 196 which is a perfect sqaure number.
FAQs on Square Roots of 194
Is the number 194 a perfect square?
No, the number 194 is not a perfect square
The square root of 194 is an irrational number and all perfect squares have integers as their square root.
Is the square root of 194 is a rational number?
No, the square root of 194 is not a rational number
Because it cannot be expressed in the form of p/q where q ≠ 0.
What is the negative square root of 194?
The negative square root of 194 is 13.9283
What is the square of 194?
The square of 194 is (194)^{2} = 37636
Can we find the square root of 194 using the repeated subtraction method?
No, we can’t find the square root of 194 via the repeated subtraction method.
Because the number 194 is not a perfect square.
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