Square Root of 221
The square root of 221 is expressed as √221 in the radical form and as (221)^{½} or (221)^{0.5} in the exponent form. The square root of 221 rounded up to 8 decimal places is 14.86606875. It is the positive solution of the equation x^{2} = 221.
 Square Root of 221: 14.866068747318506
 Square Root of 221 in exponential form: (221)^{½} or (221)^{0.5}
 Square Root of 221 in radical form: √221
1.  What Is the Square Root of 221? 
2.  Is Square Root of 221 Rational or Irrational? 
3.  How to Find the Square Root of 221? 
4.  FAQs on Square Root of 221 
5.  Important Notes on Square Root of 221 
What is the Square Root of 221?
 The square root of 221 in decimal form is 14.86606
 The square root of 221 is written as √221 in radical form.
 The square root of 221 is written as (221)^{1/2} in exponential form.
Is Square Root of 221 Rational or Irrational?
The square root of 221 is not a rational number because a rational number is defined as a number that can be represented in the form of p/q where q ≠ 0. And the square root of 221 cannot be represented in the form of p/q.
Hence, the square root of 221 is an irrational number.
How to Find the Square Root of 221?
We will now calculate the square root of 221 using the belowgiven methods:
Square Root of 221 Using Approximation Method
 Calculate the two consecutive perfect squares between which 221 lies.
The two consecutive perfect squares are 196 (14^{2}) and 225 (15^{2}).
So, the whole number part of the square root of 221 is 14  Now, for the decimal part we will use the below formula:
(Given number  Smaller perfect square) / (Greater perfect square  smaller perfect square)
= (221  196)/(225  196) = 25/29 = 0.862  Hence, the approx. value of the square root of 221 by the approximation method is 14.862
Square Root of 221 By Long Division
Now we will calculate the square root of 221 by the long division method.
 Start dividing the digits from the unit’s place in pairs of two by drawing` a line on top of them. In the case of 221, we will have two pairs 21 and 2(pairing from right).
 Now, find a number(f) whose square is ≤ 2. The value of f will be 1 as 1 × 1 = 1≤ 2.
 We get the quotient (1) and the remainder also as 1. Now, add the divisor f with itself and get the new divisor 2f (2).
 Bring down the next pair (new dividend becomes 121) and find a number (N) such that 2N × N ≤ 121. The value of N comes out to be 4.
 Now, add a decimal in the dividend (221) and quotient (14) simultaneously. Also, add 3 pairs of zero in the dividend after the decimal (221. 00 00 00) and repeat the above step for the remaining three pairs of zero.
So, we get the value of the square root of √221 = 14.866 by the long division method.
Explore square roots using illustrations and interactive examples
 Square root of 22
 Square root of 225
 Square root of 224
 Square root of 121
 Square root of 22
 Square root of 21
Important Notes
 The square root of 221 is an irrational number.
 The number 221 is not a perfect square.
 The square root of 221 is an imaginary number.
Solved Examples on Square Root of 221

Example 1: What is the % error in the value of √221 calculated via the approximation method?
Solution:
The value of √221 by the approximation method = 14.862
The actual value of the square root of 221 = 14.866
The estimated value of the square of 221 is underestimated
Error in the value of √221 = 14.866  14.862 = 0.002
% Error = (0.002/14.866) × 100 = 0.013% 
Example 2: Derick wants to find the relation between the square root of √221 and (√100 + √121). Can you assist Derick?
Solution:
The square of 221 is √221 = 14.866
And the value of (√100 + √121) = 10 + 11 = 21.
The square root of 221 is less than the (√100 + √121) by (21  14.866) = 6.134 
Example 3: Solve the equation x^{2} − 221 = 0
Solution:
x^{2}  221 = 0 i.e. x^{2} = 221
x = ±√221
Since the value of the square root of 221 is 14.866,
⇒ x = +√221 or √221 = 14.866 or 14.866.
FAQs on the Square Root of 221
What is the Value of the Square Root of 221?
The square root of 221 is 14.86606.
Why is the Square Root of 221 an Irrational Number?
Upon prime factorizing 221 i.e. 13^{1} × 17^{1}, 13 is in odd power. Therefore, the square root of 221 is irrational.
If the Square Root of 221 is 14.866. Find the Value of the Square Root of 2.21.
Let us represent √2.21 in p/q form i.e. √(221/100) = 2.21/10 = 1.487. Hence, the value of √2.21 = 1.487
Is the number 221 a Perfect Square?
The prime factorization of 221 = 13^{1} × 17^{1}. Here, the prime factor 13 is not in the pair. Therefore, 221 is not a perfect square.
What is the Value of 17 square root 221?
The square root of 221 is 14.866. Therefore, 17 √221 = 17 × 14.866 = 252.723.
What is the Square Root of 221?
The square root of 221 is an imaginary number. It can be written as √221 = √1 × √221 = i √221 = 14.866i
where i = √1 and it is called the imaginary unit.
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