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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 x² = 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

Square Root of 882

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?

Square Root of 882 by Long Division Method

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.

☛ Also Check:

Square Root of 14 - √14 = 3.74166
Square Root of 100 - √100 = 10
Square Root of 116 - √116 = 10.77033
Square Root of 1296 - √1296 = 36
Square Root of 1000 - √1000 = 31.62278
Square Root of 16 - √16 = 4
Square Root of 8 - √8 = 2.82843

Square Root of 882 Solved Examples

Example 1: Solve the equation x² − 882 = 0

Solution:

x² - 882 = 0 i.e. x² = 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 in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 3528π in²
⇒ 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 in². 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)a² = 882√3 in²
⇒ 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

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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. 2¹ × 3² × 7², 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.

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