Square Root of 148
The square root of 148 is expressed as √148 in the radical form and as (148)^{½} or (148)^{0.5} in the exponent form. The square root of 148 rounded up to 5 decimal places is 12.16553. It is the positive solution of the equation x^{2} = 148. We can express the square root of 148 in its lowest radical form as 2 √37.
 Square Root of 148: 12.165525060596439
 Square Root of 148 in exponential form: (148)^{½} or (148)^{0.5}
 Square Root of 148 in radical form: √148 or 2 √37
1.  What is the Square Root of 148? 
2.  Is Square Root of 148 Rational or Irrational? 
3.  How to Find the Square Root of 148? 
4.  FAQs on Square Root of 148 
What is the Square Root of 148?
The square root of a number is the number (integer) which when multiplied by itself results in the original number. Like 144 can be expressed as 12^{2} = 12 × 12. Here 12 is called the square root of 144 and we know that 144 is a perfect square. Nonsquare numbers also have a square root, the only difference is that they are not whole numbers. Similarly the square root of 148 is expressed as √148 in the radical form and as 148^{½} in the exponent form. The square root of 148 rounded to 4 decimal places is +12.1655, 12.1655.
 148 = a × a = 12.1655
 Then a = √148 = √(12.1655 × 12.1655)
 The square root of 148 is +12.1655 or 12.1655
 This shows that 148 is not a perfect square.
Is Square Root of 148 Rational or Irrational?
A rational number is defined as a number that can be represented in the ratio of two integers(p/q) where q ≠ 0. A number that cannot be expressed as a ratio of two integers is an irrational number. The decimal form of the irrational number is nonterminating (i.e., it never ends) and nonrecurring (i.e., the decimal part of the number never repeats a pattern). The square root of 148 cannot be written in the form of p/q. Therefore, the square root of 148 is an irrational number. √148 = 12.1655. Hence, √148 is an irrational number.
How to Find the Square Root of 148?
The square root of 148 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits 148 by putting a bar above 48 and 1 separately. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 1. This will be 1 obviously, so place 1 in the quotient and the divisors place which will result in the remainder being 0.
 Step 3: Drag down 48 beside the remainder 0. Also, add the divisor to itself and write it below.(1+1=2)
 Step 3: Find a number X such that 2X × X results in a number less than or equal to 48. The number 2 fits here so fill it next to 2 in the divisor as well as next to 1 in the quotient.
 Step 4: Find the remainder and now drag down the pair of 0s from the decimal part of the number. Adding, X to the divisor, the new divisor becomes 24.
 Step 5: Repeat this process to get the decimal places you want.
Important Notes:
 The square root of 148 is an irrational number.
 The number 148 is not a perfect square.
 The square root of 148 is an imaginary number.
 There exists a positive and negative roots of 148, +12.165 and 12.165.
 The square root of 148 in decimal form is +12.165.
 The square root of 148 is represented as √148 in radical form.
 The square root of 148 is represented as (148)^{½} in exponential form.
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Challenging Questions
 What is the negative root of 1480?
 Find the square root of 148 up to 5 decimal places?
 What is the square root of:
a) 1148
b) √14148
Square Root of 148 Solved Examples

Example 1: What are the two consecutive numbers between which the value of square root of 148 lies?
Solution:
The perfect squares closer to 148 are 144 and 169. As the square root of 144 is 12 and the square root of 169 is 13. Hence, the two consecutive numbers between which the square root of 148 lies are 12 and 13.
Therefore, the numbers are 12 and 13. 
Example 2: What number Rumi should subtract to 148 to obtain a perfect square number if the square root of the obtained number is 12, find the number. Find if the obtained number is also a perfect square.
Solution:
To find the number let us assume number = a
On subtracting 'a' we get,
148  a = (12)²
a = 148  144
a = 4
148  4 = 144.
144 is a perfect square (√144 = 12).
4 is also a perfect square number √4 = 2
The number is 4 and it is a perfect square. 
Example: If the area of a circle is 148π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 148π in^{2}
⇒ r = ±√148 in
Since radius can't be negative,
⇒ r = √148
The square root of 148 is 12.166.
⇒ r = 12.166 in
FAQs on the Square Root of 148
What is the Value of the Square Root of 148?
The square root of 148 is 12.16552.
Why is the Square Root of 148 an Irrational Number?
Upon prime factorizing 148 i.e. 2^{2} × 37^{1}, 37 is in odd power. Therefore, the square root of 148 is irrational.
What is the Value of 14 square root 148?
The square root of 148 is 12.166. Therefore, 14 √148 = 14 × 12.166 = 170.317.
What is the Square of the Square Root of 148?
The square of the square root of 148 is the number 148 itself i.e. (√148)^{2} = (148)^{2/2} = 148.
Is the number 148 a Perfect Square?
The prime factorization of 148 = 2^{2} × 37^{1}. Here, the prime factor 37 is not in the pair. Therefore, 148 is not a perfect square.
What is the Square Root of 148 in Simplest Radical Form?
We need to express 148 as the product of its prime factors i.e. 148 = 2 × 2 × 37. Therefore, √148 = √2 × 2 × 37 = 2 √37. Thus, the square root of 148 in the lowest radical form is 2 √37.
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