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Square Root of 880

The square root of 880 is expressed as √880 in the radical form and as (880)^½ or (880)^0.5 in the exponent form. The square root of 880 rounded up to 9 decimal places is 29.664793948. It is the positive solution of the equation x² = 880. We can express the square root of 880 in its lowest radical form as 4 √55.

Square Root of 880: 29.664793948382652
Square Root of 880 in exponential form: (880)^½ or (880)^0.5
Square Root of 880 in radical form: √880 or 4 √55

Square Root of 880

1.	What is the Square Root of 880?
2.	How to find the Square Root of 880?
3.	Is the Square Root of 880 Irrational?
4.	FAQs

What is the Square Root of 880?

The square root of 880, (or root 880), is the number which when multiplied by itself gives the product as 880. Therefore, the square root of 880 = √880 = 4 √55 = 29.664793948382652.

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How to Find Square Root of 880?

Square Root of 880 by Long Division Method

Value of √880 by Long Division Method

Explanation:

Forming pairs: 08 and 80
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 80, to the right of the remainder 4. The new dividend is now 480.
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 <= 480. After finding Z, together 4 and Z (9) form a new divisor 49 for the new dividend 480.
Divide 480 by 49 with the quotient as 9, giving the remainder = 480 - 49 × 9 = 480 - 441 = 39.
Now, let's find the decimal places after the quotient 29.
Bring down 00 to the right of this remainder 39. The new dividend is now 3900.
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 <= 3900. Together they form a new divisor (586) for the new dividend (3900).
Divide 3900 by 586 with the quotient as 6, giving the remainder = 3900 - 586 × 6 = 3900 - 3516 = 384.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 880.

Therefore, the square root of 880 by long division method is 29.6 approx.

Is Square Root of 880 Irrational?

The actual value of √880 is undetermined. The value of √880 up to 25 decimal places is 29.66479394838265179484559. Hence, the square root of 880 is an irrational number.

☛ Also Check:

Square Root of 676 - √676 = 26
Square Root of 92 - √92 = 9.59166
Square Root of 784 - √784 = 28
Square Root of 65 - √65 = 8.06226
Square Root of 33 - √33 = 5.74456
Square Root of 99 - √99 = 9.94987
Square Root of 841 - √841 = 29

Square Root of 880 Solved Examples

Example 1: Solve the equation x² − 880 = 0

Solution:

x² - 880 = 0 i.e. x² = 880
x = ±√880
Since the value of the square root of 880 is 29.665,
⇒ x = +√880 or -√880 = 29.665 or -29.665.
Example 2: If the area of a circle is 880π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 880π in²
⇒ r = ±√880 in
Since radius can't be negative,
⇒ r = √880
The square root of 880 is 29.665.
⇒ r = 29.665 in
Example 3: If the area of a square is 880 in². 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 = a² = 880 in²
⇒ a = ±√880 in
Since length can't be negative,
⇒ a = √880 = 29.665 in

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FAQs on the Square Root of 880

What is the Value of the Square Root of 880?

The square root of 880 is 29.66479.

Why is the Square Root of 880 an Irrational Number?

Upon prime factorizing 880 i.e. 2⁴ × 5¹ × 11¹, 5 is in odd power. Therefore, the square root of 880 is irrational.

What is the Square Root of -880?

The square root of -880 is an imaginary number. It can be written as √-880 = √-1 × √880 = i √880 = 29.664i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 880 in Simplest Radical Form?

We need to express 880 as the product of its prime factors i.e. 880 = 2 × 2 × 2 × 2 × 5 × 11. Therefore, √880 = √2 × 2 × 2 × 2 × 5 × 11 = 4 √55. Thus, the square root of 880 in the lowest radical form is 4 √55.

If the Square Root of 880 is 29.665. Find the Value of the Square Root of 8.8.

Let us represent √8.8 in p/q form i.e. √(880/100) = 8.8/10 = 2.966. Hence, the value of √8.8 = 2.966

What is the Square of the Square Root of 880?

The square of the square root of 880 is the number 880 itself i.e. (√880)² = (880)^2/2 = 880.

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