Square Root of 185
The square root of 185 is the inverse of the mathematical operation of the square of a number(m). Therefore, the number m is the square root of 185 as its product with itself results in 185. Now, we will see different ways to calculate the square root of 185 and along the way will solve some problems related to the square root of 185 as well.
 Square root of 185: √185 = 13.6014
 Square of 185: (185)^{2} = 34225
1.  What Is the Square Root of 185? 
2.  Is Square Root of 185 Rational or Irrational? 
3.  How to Find the Square Root of 185? 
4.  FAQs on Square Root of 185 
5.  Important Notes on Square Root of 185 
What is the Square Root of 185?
 The square root of 185 in decimal form is 13.6014.
 The square root of 185 can be written as (185)^{1/2} in exponential form.
 The square root of 185 is written as √185 in radical form.
 The number 185 only has two prime factors that are, 5 and 37. Hence, its square root cannot be simplified further using the prime factorization.
Is Square Root of 185 Rational or Irrational?
The square root of 185 is a nonrepeating and nonterminating number. A number is called a rational number when it can be expressed in the form of p/q where q ≠ 0 hence, the square root of 185 is an irrational number.
How to Find the Square Root of 185?
We will now find the square root of 185 using the belowgiven methods:
 Square Root of 185 Using Approximation Method
 Square Root of 185 by Long Division
Square Root of 185 Using Approximation Method
 Firstly, find two consecutive perfect squares such that 185 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 185 will be 13.
 To determine the decimal part we use the formula: (Given number  smaller perfect square) / (Greater perfect square  smaller perfect square)
= (185  169)/(196  169) = 16/27 = 0.592  So, the approx. the square root of 185 by the approximation method is 13.592.
Square Root of 185 By Long Division
Now we will calculate the square root of 185 by the long division method.
 Start pairing the digits by drawing a line on top of them from the unit’s place in pairs of two. We will have two pairs in this case (1 & 85).
 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 the next pair down (85). So, the dividend becomes 085.
 Now, find a number(y) such that 2y × y ≤ 85. The number y will be 3 as 23 × 3 = 69 ≤ 85.
 Put a decimal after the dividend and quotient simultaneously. Also, place 3 pairs of zero in the dividend part after the decimal (185. 00 00 00) and repeat the above step for the remaining three pair of zero.
So, we get the square root of √185 = 13.601 by the long division method.
Explore square roots using illustrations and interactive examples.
Important Notes:
 The square root of 185 is an irrational number.
 The square root of 185 is an imaginary number.
 The number 185 is not a perfect square.
Square Root of 185 Solved Examples

Example 1: Help Derick determine the %error in the square root of 185 calculated by the approximation method and analyze whether it is over or underestimated.
Solution:
The value of the square root of 185 is √185 = 13.601.
The value of the square root of 185 calculated by approximation method is √185 = 13.592.
As the value is less than the actual value so, it is underestimated.
Now, % error = ((13.601 – 13.592)/13.601) × 100 = 0.066%
Hence, the %error in the square root of 185 calculated by the approximation method is 0.066%. 
Example 2: A car is covering √185 miles per 5 mins. What is the speed of the car in miles/hour?
Solution:
Speed of car in miles/min = (Distance/Time) = √185/5 = √37/√5 Miles/min.
Now, speed of the car in miles/hr = speed of the car in miles/min × 60 = (√37/√5) × 60
On simplifying we get, √37 × 12√5 = 12√185 = 12 × 13.60 = 163.2 miles/hour.
FAQs on Square Roots of 185
What is the square of 185?
The square of 185 is 37225.
What is the negative square root of 185?
The negative square root of 185 is 13.6014.
Is the square root of 185 is a rational number?
No, the square root of 185 is not a rational number because it cannot be expressed in the form of p/q where q ≠ 0.
Is the number 185 a perfect square?
No, the number 185 is not a perfect square. The square root of 185 is an irrational number and all perfect squares have integers as their square root.
Can we find the square root of 185 using the repeated subtraction method?
No, we cannot find the square root of 185 using the repeated subtraction method because the number 185 is not a perfect square.