Square Root of 316
The square root of 316 is expressed as √316 in the radical form and as (316)^{½} or (316)^{0.5} in the exponent form. The square root of 316 rounded up to 10 decimal places is 17.7763888346. It is the positive solution of the equation x^{2} = 316. We can express the square root of 316 in its lowest radical form as 2 √79.
 Square Root of 316: 17.776388834631177
 Square Root of 316 in exponential form: (316)^{½} or (316)^{0.5}
 Square Root of 316 in radical form: √316 or 2 √79
1.  What is the Square Root of 316? 
2.  How to find the Square Root of 316? 
3.  Is the Square Root of 316 Irrational? 
4.  FAQs 
What is the Square Root of 316?
The square root of 316, (or root 316), is the number which when multiplied by itself gives the product as 316. Therefore, the square root of 316 = √316 = 2 √79 = 17.776388834631177.
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How to Find Square Root of 316?
Value of √316 by Long Division Method
Explanation:
 Forming pairs: 03 and 16
 Find a number Y (1) such that whose square is <= 3. Now divide 03 by 1 with quotient as 1.
 Bring down the next pair 16, to the right of the remainder 2. The new dividend is now 216.
 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 7) such that 2Z × Z <= 216. After finding Z, together 2 and Z (7) form a new divisor 27 for the new dividend 216.
 Divide 216 by 27 with the quotient as 7, giving the remainder = 216  27 × 7 = 216  189 = 27.
 Now, let's find the decimal places after the quotient 17.
 Bring down 00 to the right of this remainder 27. The new dividend is now 2700.
 Add the last digit of quotient to divisor i.e. 7 + 27 = 34. To the right of 34, find a digit Z (which is 7) such that 34Z × Z <= 2700. Together they form a new divisor (347) for the new dividend (2700).
 Divide 2700 by 347 with the quotient as 7, giving the remainder = 2700  347 × 7 = 2700  2429 = 271.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 316.
Therefore, the square root of 316 by long division method is 17.7 approximately.
Is Square Root of 316 Irrational?
The actual value of √316 is undetermined. The value of √316 up to 25 decimal places is 17.77638883463117770018288. Hence, the square root of 316 is an irrational number.
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 Square Root of 28  √28 = 5.29150
 Square Root of 225  √225 = 15
 Square Root of 250  √250 = 15.81139
Square Root of 316 Solved Examples

Example 1: Solve the equation x^{2} − 316 = 0
Solution:
x^{2}  316 = 0 i.e. x^{2} = 316
x = ±√316
Since the value of the square root of 316 is 17.776,
⇒ x = +√316 or √316 = 17.776 or 17.776. 
Example 2: If the area of a square is 316 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} = 316 in^{2}
⇒ a = ±√316 in
Since length can't be negative,
⇒ a = √316 = 17.776 in 
Example 3: If the surface area of a sphere is 1264π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 1264π in^{2}
⇒ r = ±√316 in
Since radius can't be negative,
⇒ r = √316
The square root of 316 is 17.776.
⇒ r = 17.776 in
FAQs on the Square Root of 316
What is the Value of the Square Root of 316?
The square root of 316 is 17.77638.
Why is the Square Root of 316 an Irrational Number?
Upon prime factorizing 316 i.e. 2^{2} × 79^{1}, 79 is in odd power. Therefore, the square root of 316 is irrational.
Evaluate 12 plus 7 square root 316
The given expression is 12 + 7 √316. We know that the square root of 316 is 17.776. Therefore, 12 + 7 √316 = 12 + 7 × 17.776 = 12 + 124.435 = 136.435
What is the Value of 9 square root 316?
The square root of 316 is 17.776. Therefore, 9 √316 = 9 × 17.776 = 159.987.
If the Square Root of 316 is 17.776. Find the Value of the Square Root of 3.16.
Let us represent √3.16 in p/q form i.e. √(316/100) = 3.16/10 = 1.778. Hence, the value of √3.16 = 1.778
What is the Square Root of 316 in Simplest Radical Form?
We need to express 316 as the product of its prime factors i.e. 316 = 2 × 2 × 79. Therefore, √316 = √2 × 2 × 79 = 2 √79. Thus, the square root of 316 in the lowest radical form is 2 √79.
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