Square Root of 254
The square root of 254 is expressed as √254 in the radical form and as (254)^{½} or (254)^{0.5} in the exponent form. The square root of 254 rounded up to 9 decimal places is 15.937377451. It is the positive solution of the equation x^{2} = 254.
 Square Root of 254: 15.937377450509228
 Square Root of 254 in exponential form: (254)^{½} or (254)^{0.5}
 Square Root of 254 in radical form: √254
1.  What is the Square Root of 254? 
2.  How to find the Square Root of 254? 
3.  Is the Square Root of 254 Irrational? 
4.  FAQs 
What is the Square Root of 254?
The square root of 254, (or root 254), is the number which when multiplied by itself gives the product as 254. Therefore, the square root of 254 = √254 = 15.937377450509228.
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How to Find Square Root of 254?
Value of √254 by Long Division Method
Explanation:
 Forming pairs: 02 and 54
 Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
 Bring down the next pair 54, to the right of the remainder 1. The new dividend is now 154.
 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 5) such that 2Z × Z <= 154. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 154.
 Divide 154 by 25 with the quotient as 5, giving the remainder = 154  25 × 5 = 154  125 = 29.
 Now, let's find the decimal places after the quotient 15.
 Bring down 00 to the right of this remainder 29. The new dividend is now 2900.
 Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 9) such that 30Z × Z <= 2900. Together they form a new divisor (309) for the new dividend (2900).
 Divide 2900 by 309 with the quotient as 9, giving the remainder = 2900  309 × 9 = 2900  2781 = 119.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 254.
Therefore, the square root of 254 by long division method is 15.9 approx.
Is Square Root of 254 Irrational?
The actual value of √254 is undetermined. The value of √254 up to 25 decimal places is 15.93737745050922736663116. Hence, the square root of 254 is an irrational number.
ā Also Check:
 Square Root of 784  √784 = 28
 Square Root of 25  √25 = 5
 Square Root of 240  √240 = 15.49193
 Square Root of 39  √39 = 6.24500
 Square Root of 34  √34 = 5.83095
 Square Root of 49  √49 = 7
 Square Root of 125  √125 = 11.18034
Square Root of 254 Solved Examples

Example 1: Solve the equation x^{2} − 254 = 0
Solution:
x^{2}  254 = 0 i.e. x^{2} = 254
x = ±√254
Since the value of the square root of 254 is 15.937,
⇒ x = +√254 or √254 = 15.937 or 15.937. 
Example 2: If the surface area of a cube is 1524 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} = 1524 in^{2}
⇒ a = ±√254 in
Since length can't be negative,
⇒ a = √254
We know that the square root of 254 is 15.937.
⇒ a = 15.937 in 
Example 3: If the surface area of a sphere is 1016π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 1016π in^{2}
⇒ r = ±√254 in
Since radius can't be negative,
⇒ r = √254
The square root of 254 is 15.937.
⇒ r = 15.937 in
FAQs on the Square Root of 254
What is the Value of the Square Root of 254?
The square root of 254 is 15.93737.
Why is the Square Root of 254 an Irrational Number?
Upon prime factorizing 254 i.e. 2^{1} × 127^{1}, 2 is in odd power. Therefore, the square root of 254 is irrational.
What is the Square Root of 254 in Simplest Radical Form?
We need to express 254 as the product of its prime factors i.e. 254 = 2 × 127. Therefore, as visible, the radical form of the square root of 254 cannot be simplified further. Therefore, the simplest radical form of the square root of 254 can be written as √254
What is the Square Root of 254?
The square root of 254 is an imaginary number. It can be written as √254 = √1 × √254 = i √254 = 15.937i
where i = √1 and it is called the imaginary unit.
What is the Value of 10 square root 254?
The square root of 254 is 15.937. Therefore, 10 √254 = 10 × 15.937 = 159.374.
Evaluate 19 plus 20 square root 254
The given expression is 19 + 20 √254. We know that the square root of 254 is 15.937. Therefore, 19 + 20 √254 = 19 + 20 × 15.937 = 19 + 318.748 = 337.748