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 x² = 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

• 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.

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.

We will now calculate the square root of 221 using the below-given 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 (14²) and 225 (15²).
  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

• 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.