Square Root of 204
The square root of 204 is expressed as √204 in the radical form and as (204)^{½} or (204)^{0.5} in the exponent form. The square root of 204 rounded up to 7 decimal places is 14.2828569. It is the positive solution of the equation x^{2} = 204. We can express the square root of 204 in its lowest radical form as 2 √51.
 Square Root of 204: 14.2828568570857
 Square Root of 204 in exponential form: (204)^{½} or (204)^{0.5}
 Square Root of 204 in radical form: √204 or 2 √51
1.  What is the Square Root of 204? 
2.  How to find the Square Root of 204? 
3.  Is the Square Root of 204 Irrational? 
4.  FAQs 
What is the Square Root of 204?
The square root of 204, (or root 204), is the number which when multiplied by itself gives the product as 204. Therefore, the square root of 204 = √204 = 2 √51 = 14.2828568570857.
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How to Find Square Root of 204?
Value of √204 by Long Division Method
Explanation:
 Forming pairs: 02 and 04
 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 04, to the right of the remainder 1. The new dividend is now 104.
 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 <= 104. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 104.
 Divide 104 by 24 with the quotient as 4, giving the remainder = 104  24 × 4 = 104  96 = 8.
 Now, let's find the decimal places after the quotient 14.
 Bring down 00 to the right of this remainder 8. The new dividend is now 800.
 Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 2) such that 28Z × Z <= 800. Together they form a new divisor (282) for the new dividend (800).
 Divide 800 by 282 with the quotient as 2, giving the remainder = 800  282 × 2 = 800  564 = 236.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 204.
Therefore, the square root of 204 by long division method is 14.2 approximately.
Is Square Root of 204 Irrational?
The actual value of √204 is undetermined. The value of √204 up to 25 decimal places is 14.28285685708569999599880. Hence, the square root of 204 is an irrational number.
☛ Also Check:
 Square Root of 113  √113 = 10.63015
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 Square Root of 900  √900 = 30
 Square Root of 12  √12 = 3.46410
 Square Root of 8  √8 = 2.82843
 Square Root of 72  √72 = 8.48528
Square Root of 204 Solved Examples

Example 1: Solve the equation x^{2} − 204 = 0
Solution:
x^{2}  204 = 0 i.e. x^{2} = 204
x = ±√204
Since the value of the square root of 204 is 14.283,
⇒ x = +√204 or √204 = 14.283 or 14.283. 
Example 2: If the area of a circle is 204π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 204π in^{2}
⇒ r = ±√204 in
Since radius can't be negative,
⇒ r = √204
The square root of 204 is 14.283.
⇒ r = 14.283 in 
Example 3: If the area of an equilateral triangle is 204√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} = 204√3 in^{2}
⇒ a = ±√816 in
Since length can't be negative,
⇒ a = √816 = 2 √204
We know that the square root of 204 is 14.283.
⇒ a = 28.566 in
FAQs on the Square Root of 204
What is the Value of the Square Root of 204?
The square root of 204 is 14.28285.
Why is the Square Root of 204 an Irrational Number?
Upon prime factorizing 204 i.e. 2^{2} × 3^{1} × 17^{1}, 3 is in odd power. Therefore, the square root of 204 is irrational.
Is the number 204 a Perfect Square?
The prime factorization of 204 = 2^{2} × 3^{1} × 17^{1}. Here, the prime factor 3 is not in the pair. Therefore, 204 is not a perfect square.
What is the Value of 18 square root 204?
The square root of 204 is 14.283. Therefore, 18 √204 = 18 × 14.283 = 257.091.
What is the Square Root of 204 in Simplest Radical Form?
We need to express 204 as the product of its prime factors i.e. 204 = 2 × 2 × 3 × 17. Therefore, √204 = √2 × 2 × 3 × 17 = 2 √51. Thus, the square root of 204 in the lowest radical form is 2 √51.
If the Square Root of 204 is 14.283. Find the Value of the Square Root of 2.04.
Let us represent √2.04 in p/q form i.e. √(204/100) = 2.04/10 = 1.428. Hence, the value of √2.04 = 1.428