Square Root of 882
The square root of 882 is expressed as √882 in the radical form and as (882)^{½} or (882)^{0.5} in the exponent form. The square root of 882 rounded up to 10 decimal places is 29.6984848098. It is the positive solution of the equation x^{2} = 882. We can express the square root of 882 in its lowest radical form as 21 √2.
 Square Root of 882: 29.698484809834994
 Square Root of 882 in exponential form: (882)^{½} or (882)^{0.5}
 Square Root of 882 in radical form: √882 or 21 √2
1.  What is the Square Root of 882? 
2.  How to find the Square Root of 882? 
3.  Is the Square Root of 882 Irrational? 
4.  FAQs 
What is the Square Root of 882?
The square root of 882, (or root 882), is the number which when multiplied by itself gives the product as 882. Therefore, the square root of 882 = √882 = 21 √2 = 29.698484809834994.
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How to Find Square Root of 882?
Value of √882 by Long Division Method
Explanation:
 Forming pairs: 08 and 82
 Find a number Y (2) such that whose square is <= 8. Now divide 08 by 2 with quotient as 2.
 Bring down the next pair 82, to the right of the remainder 4. The new dividend is now 482.
 Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 9) such that 4Z × Z <= 482. After finding Z, together 4 and Z (9) form a new divisor 49 for the new dividend 482.
 Divide 482 by 49 with the quotient as 9, giving the remainder = 482  49 × 9 = 482  441 = 41.
 Now, let's find the decimal places after the quotient 29.
 Bring down 00 to the right of this remainder 41. The new dividend is now 4100.
 Add the last digit of quotient to divisor i.e. 9 + 49 = 58. To the right of 58, find a digit Z (which is 6) such that 58Z × Z <= 4100. Together they form a new divisor (586) for the new dividend (4100).
 Divide 4100 by 586 with the quotient as 6, giving the remainder = 4100  586 × 6 = 4100  3516 = 584.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 882.
Therefore, the square root of 882 by long division method is 29.6 approximately.
Is Square Root of 882 Irrational?
The actual value of √882 is undetermined. The value of √882 up to 25 decimal places is 29.69848480983499602483546. Hence, the square root of 882 is an irrational number.
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 Square Root of 16  √16 = 4
 Square Root of 8  √8 = 2.82843
Square Root of 882 Solved Examples

Example 1: Solve the equation x^{2} − 882 = 0
Solution:
x^{2}  882 = 0 i.e. x^{2} = 882
x = ±√882
Since the value of the square root of 882 is 29.698,
⇒ x = +√882 or √882 = 29.698 or 29.698. 
Example 2: If the surface area of a sphere is 3528π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 3528π in^{2}
⇒ r = ±√882 in
Since radius can't be negative,
⇒ r = √882
The square root of 882 is 29.698.
⇒ r = 29.698 in 
Example 3: If the area of an equilateral triangle is 882√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} = 882√3 in^{2}
⇒ a = ±√3528 in
Since length can't be negative,
⇒ a = √3528 = 2 √882
We know that the square root of 882 is 29.698.
⇒ a = 59.397 in
FAQs on the Square Root of 882
What is the Value of the Square Root of 882?
The square root of 882 is 29.69848.
Why is the Square Root of 882 an Irrational Number?
Upon prime factorizing 882 i.e. 2^{1} × 3^{2} × 7^{2}, 2 is in odd power. Therefore, the square root of 882 is irrational.
What is the Square of the Square Root of 882?
The square of the square root of 882 is the number 882 itself i.e. (√882)^{2} = (882)^{2/2} = 882.
What is the Value of 9 square root 882?
The square root of 882 is 29.698. Therefore, 9 √882 = 9 × 29.698 = 267.286.
What is the Square Root of 882?
The square root of 882 is an imaginary number. It can be written as √882 = √1 × √882 = i √882 = 29.698i
where i = √1 and it is called the imaginary unit.
What is the Square Root of 882 in Simplest Radical Form?
We need to express 882 as the product of its prime factors i.e. 882 = 2 × 3 × 3 × 7 × 7. Therefore, √882 = √2 × 3 × 3 × 7 × 7 = 21 √2. Thus, the square root of 882 in the lowest radical form is 21 √2.