Square Root of 284
The square root of 284 is expressed as √284 in the radical form and as (284)^{½} or (284)^{0.5} in the exponent form. The square root of 284 rounded up to 5 decimal places is 16.85230. It is the positive solution of the equation x^{2} = 284. We can express the square root of 284 in its lowest radical form as 2 √71.
 Square Root of 284: 16.852299546352718
 Square Root of 284 in exponential form: (284)^{½} or (284)^{0.5}
 Square Root of 284 in radical form: √284 or 2 √71
1.  What is the Square Root of 284? 
2.  How to find the Square Root of 284? 
3.  Is the Square Root of 284 Irrational? 
4.  FAQs 
What is the Square Root of 284?
The square root of 284, (or root 284), is the number which when multiplied by itself gives the product as 284. Therefore, the square root of 284 = √284 = 2 √71 = 16.852299546352718.
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How to Find Square Root of 284?
Value of √284 by Long Division Method
Explanation:
 Forming pairs: 02 and 84
 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 84, to the right of the remainder 1. The new dividend is now 184.
 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 6) such that 2Z × Z <= 184. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 184.
 Divide 184 by 26 with the quotient as 6, giving the remainder = 184  26 × 6 = 184  156 = 28.
 Now, let's find the decimal places after the quotient 16.
 Bring down 00 to the right of this remainder 28. The new dividend is now 2800.
 Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 8) such that 32Z × Z <= 2800. Together they form a new divisor (328) for the new dividend (2800).
 Divide 2800 by 328 with the quotient as 8, giving the remainder = 2800  328 × 8 = 2800  2624 = 176.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 284.
Therefore, the square root of 284 by long division method is 16.8 approx.
Is Square Root of 284 Irrational?
The actual value of √284 is undetermined. The value of √284 up to 25 decimal places is 16.85229954635271726126828. Hence, the square root of 284 is an irrational number.
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Square Root of 284 Solved Examples

Example 1: Solve the equation x^{2} − 284 = 0
Solution:
x^{2}  284 = 0 i.e. x^{2} = 284
x = ±√284
Since the value of the square root of 284 is 16.852,
⇒ x = +√284 or √284 = 16.852 or 16.852. 
Example 2: If the area of a square is 284 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} = 284 in^{2}
⇒ a = ±√284 in
Since length can't be negative,
⇒ a = √284 = 16.852 in 
Example 3: If the area of an equilateral triangle is 284√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} = 284√3 in^{2}
⇒ a = ±√1136 in
Since length can't be negative,
⇒ a = √1136 = 2 √284
We know that the square root of 284 is 16.852.
⇒ a = 33.705 in
FAQs on the Square Root of 284
What is the Value of the Square Root of 284?
The square root of 284 is 16.85229.
Why is the Square Root of 284 an Irrational Number?
Upon prime factorizing 284 i.e. 2^{2} × 71^{1}, 71 is in odd power. Therefore, the square root of 284 is irrational.
If the Square Root of 284 is 16.852. Find the Value of the Square Root of 2.84.
Let us represent √2.84 in p/q form i.e. √(284/100) = 2.84/10 = 1.685. Hence, the value of √2.84 = 1.685
What is the Square Root of 284 in Simplest Radical Form?
We need to express 284 as the product of its prime factors i.e. 284 = 2 × 2 × 71. Therefore, √284 = √2 × 2 × 71 = 2 √71. Thus, the square root of 284 in the lowest radical form is 2 √71.
What is the Value of 10 square root 284?
The square root of 284 is 16.852. Therefore, 10 √284 = 10 × 16.852 = 168.523.
What is the Square of the Square Root of 284?
The square of the square root of 284 is the number 284 itself i.e. (√284)^{2} = (284)^{2/2} = 284.