Square Root of 156
The square root of 156 is expressed as √156 in the radical form and as (156)^{½} or (156)^{0.5} in the exponent form. The square root of 156 rounded up to 5 decimal places is 12.49000. It is the positive solution of the equation x^{2} = 156. We can express the square root of 156 in its lowest radical form as 2 √39.
 Square Root of 156: 12.489995996796797
 Square Root of 156 in exponential form: (156)^{½} or (156)^{0.5}
 Square Root of 156 in radical form: √156 or 2 √39
1.  What is the Square Root of 156? 
2.  How to find the Square Root of 156? 
3.  Is the Square Root of 156 Irrational? 
4.  FAQs 
What is the Square Root of 156?
The square root of 156, (or root 156), is the number which when multiplied by itself gives the product as 156. Therefore, the square root of 156 = √156 = 2 √39 = 12.489995996796797.
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How to Find Square Root of 156?
Value of √156 by Long Division Method
Explanation:
 Forming pairs: 01 and 56
 Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
 Bring down the next pair 56, to the right of the remainder 0. The new dividend is now 56.
 Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 2) such that 2Z × Z <= 56. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 56.
 Divide 56 by 22 with the quotient as 2, giving the remainder = 56  22 × 2 = 56  44 = 12.
 Now, let's find the decimal places after the quotient 12.
 Bring down 00 to the right of this remainder 12. The new dividend is now 1200.
 Add the last digit of quotient to divisor i.e. 2 + 22 = 24. To the right of 24, find a digit Z (which is 4) such that 24Z × Z <= 1200. Together they form a new divisor (244) for the new dividend (1200).
 Divide 1200 by 244 with the quotient as 4, giving the remainder = 1200  244 × 4 = 1200  976 = 224.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 156.
Therefore, the square root of 156 by long division method is 12.4 approximately.
Is Square Root of 156 Irrational?
The actual value of √156 is undetermined. The value of √156 up to 25 decimal places is 12.48999599679679641169379. Hence, the square root of 156 is an irrational number.
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 Square Root of 288  √288 = 16.97056
 Square Root of 116  √116 = 10.77033
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Square Root of 156 Solved Examples

Example 1: Solve the equation x^{2} − 156 = 0
Solution:
x^{2}  156 = 0 i.e. x^{2} = 156
x = ±√156
Since the value of the square root of 156 is 12.490,
⇒ x = +√156 or √156 = 12.490 or 12.490. 
Example 2: If the surface area of a cube is 936 in^{2}. Find the length of the side of the cube.
Solution:
Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a^{2} = 936 in^{2}
⇒ a = ±√156 in
Since length can't be negative,
⇒ a = √156
We know that the square root of 156 is 12.490.
⇒ a = 12.490 in 
Example 3: If the surface area of a sphere is 624π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 624π in^{2}
⇒ r = ±√156 in
Since radius can't be negative,
⇒ r = √156
The square root of 156 is 12.490.
⇒ r = 12.490 in
FAQs on the Square Root of 156
What is the Value of the Square Root of 156?
The square root of 156 is 12.48999.
Why is the Square Root of 156 an Irrational Number?
Upon prime factorizing 156 i.e. 2^{2} × 3^{1} × 13^{1}, 3 is in odd power. Therefore, the square root of 156 is irrational.
What is the Square Root of 156 in Simplest Radical Form?
We need to express 156 as the product of its prime factors i.e. 156 = 2 × 2 × 3 × 13. Therefore, √156 = √2 × 2 × 3 × 13 = 2 √39. Thus, the square root of 156 in the lowest radical form is 2 √39.
What is the Square Root of 156?
The square root of 156 is an imaginary number. It can be written as √156 = √1 × √156 = i √156 = 12.489i
where i = √1 and it is called the imaginary unit.
Is the number 156 a Perfect Square?
The prime factorization of 156 = 2^{2} × 3^{1} × 13^{1}. Here, the prime factor 3 is not in the pair. Therefore, 156 is not a perfect square.
What is the Value of 8 square root 156?
The square root of 156 is 12.490. Therefore, 8 √156 = 8 × 12.490 = 99.920.