Square Root of 201
The square root of 201 is expressed as √201 in the radical form and as (201)^{½} or (201)^{0.5} in the exponent form. The square root of 201 rounded up to 10 decimal places is 14.1774468788. It is the positive solution of the equation x^{2} = 201.
 Square Root of 201: 14.177446878757825
 Square Root of 201 in exponential form: (201)^{½} or (201)^{0.5}
 Square Root of 201 in radical form: √201
1.  What is the Square Root of 201? 
2.  How to find the Square Root of 201? 
3.  Is the Square Root of 201 Irrational? 
4.  FAQs 
What is the Square Root of 201?
The square root of 201, (or root 201), is the number which when multiplied by itself gives the product as 201. Therefore, the square root of 201 = √201 = 14.177446878757825.
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How to Find Square Root of 201?
Value of √201 by Long Division Method
Explanation:
 Forming pairs: 02 and 01
 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 01, to the right of the remainder 1. The new dividend is now 101.
 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 <= 101. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 101.
 Divide 101 by 24 with the quotient as 4, giving the remainder = 101  24 × 4 = 101  96 = 5.
 Now, let's find the decimal places after the quotient 14.
 Bring down 00 to the right of this remainder 5. The new dividend is now 500.
 Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 1) such that 28Z × Z <= 500. Together they form a new divisor (281) for the new dividend (500).
 Divide 500 by 281 with the quotient as 1, giving the remainder = 500  281 × 1 = 500  281 = 219.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 201.
Therefore, the square root of 201 by long division method is 14.1 approx.
Is Square Root of 201 Irrational?
The actual value of √201 is undetermined. The value of √201 up to 25 decimal places is 14.17744687875782520295562. Hence, the square root of 201 is an irrational number.
☛ Also Check:
 Square Root of 45  √45 = 6.70820
 Square Root of 100  √100 = 10
 Square Root of 10  √10 = 3.16228
 Square Root of 72  √72 = 8.48528
 Square Root of 116  √116 = 10.77033
 Square Root of 320  √320 = 17.88854
 Square Root of 784  √784 = 28
Square Root of 201 Solved Examples

Example 1: Solve the equation x^{2} − 201 = 0
Solution:
x^{2}  201 = 0 i.e. x^{2} = 201
x = ±√201
Since the value of the square root of 201 is 14.177,
⇒ x = +√201 or √201 = 14.177 or 14.177. 
Example 2: If the area of an equilateral triangle is 201√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} = 201√3 in^{2}
⇒ a = ±√804 in
Since length can't be negative,
⇒ a = √804 = 2 √201
We know that the square root of 201 is 14.177.
⇒ a = 28.355 in 
Example 3: If the area of a square is 201 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} = 201 in^{2}
⇒ a = ±√201 in
Since length can't be negative,
⇒ a = √201 = 14.177 in
FAQs on the Square Root of 201
What is the Value of the Square Root of 201?
The square root of 201 is 14.17744.
Why is the Square Root of 201 an Irrational Number?
Upon prime factorizing 201 i.e. 3^{1} × 67^{1}, 3 is in odd power. Therefore, the square root of 201 is irrational.
What is the Value of 19 square root 201?
The square root of 201 is 14.177. Therefore, 19 √201 = 19 × 14.177 = 269.371.
Evaluate 12 plus 20 square root 201
The given expression is 12 + 20 √201. We know that the square root of 201 is 14.177. Therefore, 12 + 20 √201 = 12 + 20 × 14.177 = 12 + 283.549 = 295.549
Is the number 201 a Perfect Square?
The prime factorization of 201 = 3^{1} × 67^{1}. Here, the prime factor 3 is not in the pair. Therefore, 201 is not a perfect square.
If the Square Root of 201 is 14.177. Find the Value of the Square Root of 2.01.
Let us represent √2.01 in p/q form i.e. √(201/100) = 2.01/10 = 1.418. Hence, the value of √2.01 = 1.418