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Square Root of 1080

The square root of 1080 is expressed as √1080 in the radical form and as (1080)^½ or (1080)^0.5 in the exponent form. The square root of 1080 rounded up to 5 decimal places is 32.86335. It is the positive solution of the equation x² = 1080. We can express the square root of 1080 in its lowest radical form as 6 √30.

Square Root of 1080: 32.863353450309965
Square Root of 1080 in exponential form: (1080)^½ or (1080)^0.5
Square Root of 1080 in radical form: √1080 or 6 √30

Square Root of 1080

1.	What is the Square Root of 1080?
2.	How to find the Square Root of 1080?
3.	Is the Square Root of 1080 Irrational?
4.	FAQs

What is the Square Root of 1080?

The square root of 1080, (or root 1080), is the number which when multiplied by itself gives the product as 1080. Therefore, the square root of 1080 = √1080 = 6 √30 = 32.863353450309965.

☛ Check: Square Root Calculator

How to Find Square Root of 1080?

Square Root of 1080 by Long Division Method

Value of √1080 by Long Division Method

Explanation:

Forming pairs: 10 and 80
Find a number Y (3) such that whose square is <= 10. Now divide 10 by 3 with quotient as 3.
Bring down the next pair 80, to the right of the remainder 1. The new dividend is now 180.
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 2) such that 6Z × Z <= 180. After finding Z, together 6 and Z (2) form a new divisor 62 for the new dividend 180.
Divide 180 by 62 with the quotient as 2, giving the remainder = 180 - 62 × 2 = 180 - 124 = 56.
Now, let's find the decimal places after the quotient 32.
Bring down 00 to the right of this remainder 56. The new dividend is now 5600.
Add the last digit of quotient to divisor i.e. 2 + 62 = 64. To the right of 64, find a digit Z (which is 8) such that 64Z × Z <= 5600. Together they form a new divisor (648) for the new dividend (5600).
Divide 5600 by 648 with the quotient as 8, giving the remainder = 5600 - 648 × 8 = 5600 - 5184 = 416.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1080.

Therefore, the square root of 1080 by long division method is 32.8 approximately.

Is Square Root of 1080 Irrational?

The actual value of √1080 is undetermined. The value of √1080 up to 25 decimal places is 32.86335345030996680741819. Hence, the square root of 1080 is an irrational number.

☛ Also Check:

Square Root of 30 - √30 = 5.47723
Square Root of 125 - √125 = 11.18034
Square Root of 2 - √2 = 1.41421
Square Root of 33 - √33 = 5.74456
Square Root of 14 - √14 = 3.74166
Square Root of 60 - √60 = 7.74597
Square Root of 8 - √8 = 2.82843

Square Root of 1080 Solved Examples

Example 1: Solve the equation x² − 1080 = 0

Solution:

x² - 1080 = 0 i.e. x² = 1080
x = ±√1080
Since the value of the square root of 1080 is 32.863,
⇒ x = +√1080 or -√1080 = 32.863 or -32.863.
Example 2: If the area of a circle is 1080π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1080π in²
⇒ r = ±√1080 in
Since radius can't be negative,
⇒ r = √1080
The square root of 1080 is 32.863.
⇒ r = 32.863 in
Example 3: If the area of an equilateral triangle is 1080√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 = 1080√3 in²
⇒ a = ±√4320 in
Since length can't be negative,
⇒ a = √4320 = 2 √1080
We know that the square root of 1080 is 32.863.
⇒ a = 65.727 in

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FAQs on the Square Root of 1080

What is the Value of the Square Root of 1080?

The square root of 1080 is 32.86335.

Why is the Square Root of 1080 an Irrational Number?

Upon prime factorizing 1080 i.e. 2³ × 3³ × 5¹, 2 is in odd power. Therefore, the square root of 1080 is irrational.

What is the Value of 4 square root 1080?

The square root of 1080 is 32.863. Therefore, 4 √1080 = 4 × 32.863 = 131.453.

What is the Square Root of -1080?

The square root of -1080 is an imaginary number. It can be written as √-1080 = √-1 × √1080 = i √1080 = 32.863i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 1080 is 32.863. Find the Value of the Square Root of 10.8.

Let us represent √10.8 in p/q form i.e. √(1080/100) = 10.8/10 = 3.286. Hence, the value of √10.8 = 3.286

What is the Square of the Square Root of 1080?

The square of the square root of 1080 is the number 1080 itself i.e. (√1080)² = (1080)^2/2 = 1080.

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