Square Root of 149
The square root of 149 is expressed as √149 in the radical form and as (149)^{½} or (149)^{0.5} in the exponent form. The square root of 149 rounded up to 5 decimal places is 12.20656. It is the positive solution of the equation x^{2} = 149.
 Square Root of 149: 12.206555615733702
 Square Root of 149 in exponential form: (149)^{½} or (149)^{0.5}
 Square Root of 149 in radical form: √149
1.  What Is the Square Root of 149? 
2.  Is Square Root of 149 Rational or Irrational? 
3.  How to Find the Square Root of 149? 
4.  FAQs on Square Root of 149 
5.  Important Notes on Square Root of 149 
What Is the Square Root of 149?
 The square root of 149 is written as (149)^{1/2} in the exponential form.
 The square root of 149 is written as √149 in the radical form.
 The square root of 149 in the decimal form is 12.2065
Is Square Root of 149 Rational or Irrational?
The square root of 149 is not an integer.
A rational number is defined as a number that can be represented in the ratio of two integers (p/q) where q ≠ 0. Since the square root of 149 cannot be written in the form of p/q, it is an irrational number.
How to Find the Square Root of 149?
We will now calculate the square root of 149 using the following methods:
Square Root of 149 Using Approximation Method
 Find two consecutive perfect squares between which 149 lies.
In the case of 149, the perfect squares are 144 (12^{2}) and 169 (13^{2}).
Thus, the whole number part of the square root of 149 is 12.  Now, for the decimal part, we will use the below formula:
(Given number – Smaller perfect square) / (Greater perfect square – smaller perfect square)
= (149 – 144)/(169 – 144) = 5/25 = 0.20  Hence, the approx. value of the square root of 149 by the approximation method is 12.20
Square Root of 149 By Long Division
With the help of the following steps, we can calculate the square root of 149 by the long division method.
 Start pairing the digits by placing a bar on top of them from the unit’s place in pairs of two. In the case of 149, we will have two pairs 49 and 1(pairing from the right).
 Now, find a number(N) whose square is ≤ 1. The value of N will be 1 as 1 × 1 = 1≤ 1.
 We get the quotient (1). Add the divisor N (1) with itself and we get the new divisor as 2N (2).
 Drag the next pair of numbers down. The new dividend is 049. Find a number (q) such that 2q × q ≤ 49. The value of q will be 2.
 Now, put a decimal in the dividend at the end of 149 and in the quotient at the end of 12. Also, place 3 pairs of zeros in the dividend after the decimal.
Repeat the above steps for the remaining three pairs of zero.
So, we get the value of the square root of √149 = 12.206 by the long division method.
Explore square roots using illustrations and interactive examples:
Important Notes:
 The square root of 149 is an irrational number.
 The number 149 is not a perfect square.
 The square root of 149 is an imaginary number.
Square Root of 149 Solved Examples

Example 1: What is the % error in the value of √149 calculated by the approximation method?
Solution:
The value of √149 by the approximation method = 12.2000
The actual value of the square root of 149 = 12.2065
Error in the value of √149 = 12.2065 – 12.2000 = 0.0065
% Error = (0.0065/12.2065) × 100 = 0.053% 
Example 2: √149 + 4√149 is the square root of which integer?
Solution:
The value of √149 + 4√149 = 5√149
We know that 5√149 = √(149 × 5 × 5 ) = √3725
Therefore, √149 + 4√149 is the square root of 3725. 
Example: If the area of a circle is 149π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 149π in^{2}
⇒ r = ±√149 in
Since radius can't be negative,
⇒ r = √149
The square root of 149 is 12.207.
⇒ r = 12.207 in
FAQs on the Square Root of 149
What is the Value of the Square Root of 149?
The square root of 149 is 12.20655.
Why is the Square Root of 149 an Irrational Number?
The number 149 is prime. This implies that the number 149 is pairless and is not in the power of 2. Therefore, the square root of 149 is irrational.
What is the Square Root of 149 in Simplest Radical Form?
The number 149 is a prime number. This implies that the number 149 is pairless and is not in the power of 2. Therefore, the radical form of square root of 149 cannot be simplified further.
Evaluate 16 plus 9 square root 149
The given expression is 16 + 9 √149. We know that the square root of 149 is 12.207. Therefore, 16 + 9 √149 = 16 + 9 × 12.207 = 16 + 109.859 = 125.859
Is the number 149 a Perfect Square?
The number 149 is prime. This implies that the square root of 149 cannot be expressed as a product of two equal integers. Therefore, the number 149 is not a perfect square.
What is the Square Root of 149?
The square root of 149 is an imaginary number. It can be written as √149 = √1 × √149 = i √149 = 12.206i
where i = √1 and it is called the imaginary unit.
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