Square Root of 218
The square root of 218 is expressed as √218 in the radical form and as (218)^{½} or (218)^{0.5} in the exponent form. The square root of 218 rounded up to 9 decimal places is 14.764823060. It is the positive solution of the equation x^{2} = 218.
 Square Root of 218: 14.7648230602334
 Square Root of 218 in exponential form: (218)^{½} or (218)^{0.5}
 Square Root of 218 in radical form: √218
1.  What is the Square Root of 218? 
2.  How to find the Square Root of 218? 
3.  Is the Square Root of 218 Irrational? 
4.  FAQs 
What is the Square Root of 218?
The square root of 218, (or root 218), is the number which when multiplied by itself gives the product as 218. Therefore, the square root of 218 = √218 = 14.7648230602334.
☛ Check: Square Root Calculator
How to Find Square Root of 218?
Value of √218 by Long Division Method
Explanation:
 Forming pairs: 02 and 18
 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 18, to the right of the remainder 1. The new dividend is now 118.
 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 4) such that 2Z × Z <= 118. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 118.
 Divide 118 by 24 with the quotient as 4, giving the remainder = 118  24 × 4 = 118  96 = 22.
 Now, let's find the decimal places after the quotient 14.
 Bring down 00 to the right of this remainder 22. The new dividend is now 2200.
 Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 7) such that 28Z × Z <= 2200. Together they form a new divisor (287) for the new dividend (2200).
 Divide 2200 by 287 with the quotient as 7, giving the remainder = 2200  287 × 7 = 2200  2009 = 191.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 218.
Therefore, the square root of 218 by long division method is 14.7 approx.
Is Square Root of 218 Irrational?
The actual value of √218 is undetermined. The value of √218 up to 25 decimal places is 14.76482306023340057554152. Hence, the square root of 218 is an irrational number.
☛ Also Check:
 Square Root of 256  √256 = 16
 Square Root of 676  √676 = 26
 Square Root of 39  √39 = 6.24500
 Square Root of 52  √52 = 7.21110
 Square Root of 120  √120 = 10.95445
 Square Root of 77  √77 = 8.77496
 Square Root of 96  √96 = 9.79796
Square Root of 218 Solved Examples

Example 1: Solve the equation x^{2} − 218 = 0
Solution:
x^{2}  218 = 0 i.e. x^{2} = 218
x = ±√218
Since the value of the square root of 218 is 14.765,
⇒ x = +√218 or √218 = 14.765 or 14.765. 
Example 2: If the area of a square is 218 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} = 218 in^{2}
⇒ a = ±√218 in
Since length can't be negative,
⇒ a = √218 = 14.765 in 
Example 3: If the area of an equilateral triangle is 218√3 in^{2}. Find the length of one of the sides of the triangle.
Solution:
Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a^{2} = 218√3 in^{2}
⇒ a = ±√872 in
Since length can't be negative,
⇒ a = √872 = 2 √218
We know that the square root of 218 is 14.765.
⇒ a = 29.530 in
FAQs on the Square Root of 218
What is the Value of the Square Root of 218?
The square root of 218 is 14.76482.
Why is the Square Root of 218 an Irrational Number?
Upon prime factorizing 218 i.e. 2^{1} × 109^{1}, 2 is in odd power. Therefore, the square root of 218 is irrational.
Is the number 218 a Perfect Square?
The prime factorization of 218 = 2^{1} × 109^{1}. Here, the prime factor 2 is not in the pair. Therefore, 218 is not a perfect square.
What is the Square Root of 218 in Simplest Radical Form?
We need to express 218 as the product of its prime factors i.e. 218 = 2 × 109. Therefore, as visible, the radical form of the square root of 218 cannot be simplified further. Therefore, the simplest radical form of the square root of 218 can be written as √218
What is the Square of the Square Root of 218?
The square of the square root of 218 is the number 218 itself i.e. (√218)^{2} = (218)^{2/2} = 218.
Evaluate 11 plus 11 square root 218
The given expression is 11 + 11 √218. We know that the square root of 218 is 14.765. Therefore, 11 + 11 √218 = 11 + 11 × 14.765 = 11 + 162.413 = 173.413