Square Root of 999
The square root of 999 is expressed as √999 in the radical form and as (999)^{½} or (999)^{0.5} in the exponent form. The square root of 999 rounded up to 5 decimal places is 31.60696. It is the positive solution of the equation x^{2} = 999. We can express the square root of 999 in its lowest radical form as 3 √111.
 Square Root of 999: 31.606961258558215
 Square Root of 999 in exponential form: (999)^{½} or (999)^{0.5}
 Square Root of 999 in radical form: √999 or 3 √111
1.  What is the Square Root of 999? 
2.  How to find the Square Root of 999? 
3.  Is the Square Root of 999 Irrational? 
4.  FAQs 
What is the Square Root of 999?
The square root of 999, (or root 999), is the number which when multiplied by itself gives the product as 999. Therefore, the square root of 999 = √999 = 3 √111 = 31.606961258558215.
☛ Check: Square Root Calculator
How to Find Square Root of 999?
Value of √999 by Long Division Method
Explanation:
 Forming pairs: 09 and 99
 Find a number Y (3) such that whose square is <= 9. Now divide 09 by 3 with quotient as 3.
 Bring down the next pair 99, to the right of the remainder 0. The new dividend is now 99.
 Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 1) such that 6Z × Z <= 99. After finding Z, together 6 and Z (1) form a new divisor 61 for the new dividend 99.
 Divide 99 by 61 with the quotient as 1, giving the remainder = 99  61 × 1 = 99  61 = 38.
 Now, let's find the decimal places after the quotient 31.
 Bring down 00 to the right of this remainder 38. The new dividend is now 3800.
 Add the last digit of quotient to divisor i.e. 1 + 61 = 62. To the right of 62, find a digit Z (which is 6) such that 62Z × Z <= 3800. Together they form a new divisor (626) for the new dividend (3800).
 Divide 3800 by 626 with the quotient as 6, giving the remainder = 3800  626 × 6 = 3800  3756 = 44.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 999.
Therefore, the square root of 999 by long division method is 31.6 approx.
Is Square Root of 999 Irrational?
The actual value of √999 is undetermined. The value of √999 up to 25 decimal places is 31.60696125855821654520421. Hence, the square root of 999 is an irrational number.
☛ Also Check:
 Square Root of 361  √361 = 19
 Square Root of 1296  √1296 = 36
 Square Root of 23  √23 = 4.79583
 Square Root of 100  √100 = 10
 Square Root of 54  √54 = 7.34847
 Square Root of 900  √900 = 30
 Square Root of 60  √60 = 7.74597
Square Root of 999 Solved Examples

Example 1: Solve the equation x^{2} − 999 = 0
Solution:
x^{2}  999 = 0 i.e. x^{2} = 999
x = ±√999
Since the value of the square root of 999 is 31.607,
⇒ x = +√999 or √999 = 31.607 or 31.607. 
Example 2: If the area of a circle is 999π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 999π in^{2}
⇒ r = ±√999 in
Since radius can't be negative,
⇒ r = √999
The square root of 999 is 31.607.
⇒ r = 31.607 in 
Example 3: If the area of an equilateral triangle is 999√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} = 999√3 in^{2}
⇒ a = ±√3996 in
Since length can't be negative,
⇒ a = √3996 = 2 √999
We know that the square root of 999 is 31.607.
⇒ a = 63.214 in
FAQs on the Square Root of 999
What is the Value of the Square Root of 999?
The square root of 999 is 31.60696.
Why is the Square Root of 999 an Irrational Number?
Upon prime factorizing 999 i.e. 3^{3} × 37^{1}, 3 is in odd power. Therefore, the square root of 999 is irrational.
What is the Square Root of 999 in Simplest Radical Form?
We need to express 999 as the product of its prime factors i.e. 999 = 3 × 3 × 3 × 37. Therefore, √999 = √3 × 3 × 3 × 37 = 3 √111. Thus, the square root of 999 in the lowest radical form is 3 √111.
What is the Square of the Square Root of 999?
The square of the square root of 999 is the number 999 itself i.e. (√999)^{2} = (999)^{2/2} = 999.
If the Square Root of 999 is 31.607. Find the Value of the Square Root of 9.99.
Let us represent √9.99 in p/q form i.e. √(999/100) = 9.99/10 = 3.161. Hence, the value of √9.99 = 3.161
What is the Square Root of 999?
The square root of 999 is an imaginary number. It can be written as √999 = √1 × √999 = i √999 = 31.606i
where i = √1 and it is called the imaginary unit.
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