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 x² = 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

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 12² = 12 × 12. Here 12 is called the square root of 144 and we know that 144 is a perfect square. Non-square 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.

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 non-terminating (i.e., it never ends) and non-recurring (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.

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.

• 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.

Explore Square roots using illustrations and interactive examples

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• 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