Square Root of 286
The square root of 286 is expressed as √286 in the radical form and as (286)^{½} or (286)^{0.5} in the exponent form. The square root of 286 rounded up to 6 decimal places is 16.911535. It is the positive solution of the equation x^{2} = 286.
 Square Root of 286: 16.911534525287763
 Square Root of 286 in exponential form: (286)^{½} or (286)^{0.5}
 Square Root of 286 in radical form: √286
1.  What is the Square Root of 286? 
2.  How to find the Square Root of 286? 
3.  Is the Square Root of 286 Irrational? 
4.  FAQs 
What is the Square Root of 286?
The square root of 286, (or root 286), is the number which when multiplied by itself gives the product as 286. Therefore, the square root of 286 = √286 = 16.911534525287763.
ā Check: Square Root Calculator
How to Find Square Root of 286?
Value of √286 by Long Division Method
Explanation:
 Forming pairs: 02 and 86
 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 86, to the right of the remainder 1. The new dividend is now 186.
 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 6) such that 2Z × Z <= 186. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 186.
 Divide 186 by 26 with the quotient as 6, giving the remainder = 186  26 × 6 = 186  156 = 30.
 Now, let's find the decimal places after the quotient 16.
 Bring down 00 to the right of this remainder 30. The new dividend is now 3000.
 Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 9) such that 32Z × Z <= 3000. Together they form a new divisor (329) for the new dividend (3000).
 Divide 3000 by 329 with the quotient as 9, giving the remainder = 3000  329 × 9 = 3000  2961 = 39.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 286.
Therefore, the square root of 286 by long division method is 16.9 approximately.
Is Square Root of 286 Irrational?
The actual value of √286 is undetermined. The value of √286 up to 25 decimal places is 16.91153452528776289817252. Hence, the square root of 286 is an irrational number.
ā Also Check:
 Square Root of 22  √22 = 4.69042
 Square Root of 63  √63 = 7.93725
 Square Root of 33  √33 = 5.74456
 Square Root of 200  √200 = 14.14214
 Square Root of 49  √49 = 7
 Square Root of 45  √45 = 6.70820
 Square Root of 90  √90 = 9.48683
Square Root of 286 Solved Examples

Example 1: Solve the equation x^{2} − 286 = 0
Solution:
x^{2}  286 = 0 i.e. x^{2} = 286
x = ±√286
Since the value of the square root of 286 is 16.912,
⇒ x = +√286 or √286 = 16.912 or 16.912. 
Example 2: If the surface area of a sphere is 1144π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 1144π in^{2}
⇒ r = ±√286 in
Since radius can't be negative,
⇒ r = √286
The square root of 286 is 16.912.
⇒ r = 16.912 in 
Example 3: If the area of a square is 286 in^{2}. Find the length of the side of the square.
Solution:
Let 'a' be the length of the side of the square.
⇒ Area of the square = a^{2} = 286 in^{2}
⇒ a = ±√286 in
Since length can't be negative,
⇒ a = √286 = 16.912 in
FAQs on the Square Root of 286
What is the Value of the Square Root of 286?
The square root of 286 is 16.91153.
Why is the Square Root of 286 an Irrational Number?
Upon prime factorizing 286 i.e. 2^{1} × 11^{1} × 13^{1}, 2 is in odd power. Therefore, the square root of 286 is irrational.
What is the Square Root of 286?
The square root of 286 is an imaginary number. It can be written as √286 = √1 × √286 = i √286 = 16.911i
where i = √1 and it is called the imaginary unit.
What is the Value of 13 square root 286?
The square root of 286 is 16.912. Therefore, 13 √286 = 13 × 16.912 = 219.850.
Is the number 286 a Perfect Square?
The prime factorization of 286 = 2^{1} × 11^{1} × 13^{1}. Here, the prime factor 2 is not in the pair. Therefore, 286 is not a perfect square.
If the Square Root of 286 is 16.912. Find the Value of the Square Root of 2.86.
Let us represent √2.86 in p/q form i.e. √(286/100) = 2.86/10 = 1.691. Hence, the value of √2.86 = 1.691