Square Root of 216
The square root of 216 is a number which when multiplied by itself, results in the number 216. The square root is an integral part of math that everyone must learn. We will learn how to calculate the square root of 216 and look at a few problems to help us understand this topic.
 Square Root of 216: √216 = 14.6969384...
 Square of 216: 216^{2} = 26896
1.  What Is the Square Root of 216? 
2.  Is Square Root of 216 Rational or Irrational? 
3.  How to Find the Square Root of 216? 
4.  FAQs on Square Root of 216 
What Is the Square Root of 216?
The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The multiple ways of expressing square root of 216 are:
 Radical form: √216 = 6√6
 Decimal form: 14.697
 Exponent form: (216)^{1/2}
Is Square Root of 216 Rational or Irrational?
 216 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
 Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 216 is an irrational number.
How to Find the Square Root of 216?
There are only 2 ways to find the square root of 216:
 Long Division Method
 Prime Factorization
One can find out other methods by clicking here.
Long Division Method
The square root of 216 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits 216 by putting a bar above 16 and 1 separately. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 2. This will be 1 obviously, so place 1 in the quotient and the divisors place which will result in the remainder being 1.
 Step 3: Drag down 16 beside the remainder 1. Also, add the divisor to itself and write it below.(1+1=2)
 Step 4: Find a number X such that 2X × X results in a number less than or equal to 116. The number 4 fits here so fill it next to 2 in the divisor as well as next to 1 in the quotient.
 Step 5: Find the remainder and now drag down the pair of 0s from the decimal part of the number. Adding, X to the divisor, the new divisor becomes 28.
 Step 6: Repeat this process to get the decimal places you want.
Therefore, the square root of 216 = 14.697.
Prime Factorization
 For finding the square root of 216, we shall first express it in terms of its prime factors. 216 can be expressed as 216 = 2 × 2 × 2 × 3 × 3 × 3.
 This can be reduced further to 216 = 2^{3} × 3^{3}
 Finally, to find the root of this from here it is very easy,
√216 = √(2^{3} × 3^{3}) = 6√(2 × 3) = 6√6 = 14.697
Therefore, the Square Root of 216 ≅ 14.697.
Explore Square roots using illustrations and interactive examples
Challenging Questions
 What is the square root of
 21600
 2.16
 Express square root of 0.021600 in terms of square root of 216.
Square Root of 216 Solved Examples

Example 1: Amy wants to calculate the side length of his square garden in her home. It has an area of 216 square feet.
Solution:
Let us assume that the length of the garden is x feet. Then the area of the garden is x^{2} square feet. By the given information:
x^{2} = 216
x = √216 = 14.697
The final answer is rounded to the nearest tenth. Hence, the length of the room is 14.7 feet. 
Example 2: What is the radius of a circle having an area of 512π square centimetres?
Solution:
The area is found using the formula of the area of a circle, which is πr^{2}. By the given information,
πr^{2} = 512π
r^{2} = 216 × 2
r = √2 × √216 = √2 × 14.7 = 20.78 ≅ 20.8
Therefore, the radius of the circle is 20.8 cm approximately.
FAQs on Square Root of 216
What is the prime factorization of 216?
The prime factorization of 216 is 2^{3} × 3^{3}.
Is 216 a perfect square root?
216 is not a perfect square. 216 is a natural number, but since there is no other natural number that can be squared to result in the number 216, it is NOT a perfect square.
What is the decimal value of the square root of 216?
The decimal value of the square root of 216 is 14.697.
Is the square root of 216 a rational number?
No, the square root of 216 is not a rational number since the square root of 216 is nonterminating and cannot be represented in the form of p/q.
Is 216 a perfect cube root?
The cube root of 216 is 6. This is because 6 squared is 36, and 36 times 6 is 216. Therefore, it is a perfect cube root.
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