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Square Root of 440

The square root of 440 is expressed as √440 in the radical form and as (440)^½ or (440)^0.5 in the exponent form. The square root of 440 rounded up to 6 decimal places is 20.976177. It is the positive solution of the equation x² = 440. We can express the square root of 440 in its lowest radical form as 2 √110.

Square Root of 440: 20.97617696340303
Square Root of 440 in exponential form: (440)^½ or (440)^0.5
Square Root of 440 in radical form: √440 or 2 √110

Square Root of 440

1.	What is the Square Root of 440?
2.	How to find the Square Root of 440?
3.	Is the Square Root of 440 Irrational?
4.	FAQs

What is the Square Root of 440?

The square root of 440, (or root 440), is the number which when multiplied by itself gives the product as 440. Therefore, the square root of 440 = √440 = 2 √110 = 20.97617696340303.

☛ Check: Square Root Calculator

How to Find Square Root of 440?

Square Root of 440 by Long Division Method

Value of √440 by Long Division Method

Explanation:

Forming pairs: 04 and 40
Find a number Y (2) such that whose square is <= 4. Now divide 04 by 2 with quotient as 2.
Bring down the next pair 40, to the right of the remainder 0. The new dividend is now 40.
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 0) such that 4Z × Z <= 40. After finding Z, together 4 and Z (0) form a new divisor 40 for the new dividend 40.
Divide 40 by 40 with the quotient as 0, giving the remainder = 40 - 40 × 0 = 40 - 0 = 40.
Now, let's find the decimal places after the quotient 20.
Bring down 00 to the right of this remainder 40. The new dividend is now 4000.
Add the last digit of quotient to divisor i.e. 0 + 40 = 40. To the right of 40, find a digit Z (which is 9) such that 40Z × Z <= 4000. Together they form a new divisor (409) for the new dividend (4000).
Divide 4000 by 409 with the quotient as 9, giving the remainder = 4000 - 409 × 9 = 4000 - 3681 = 319.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 440.

Therefore, the square root of 440 by long division method is 20.9 approximately.

Is Square Root of 440 Irrational?

The actual value of √440 is undetermined. The value of √440 up to 25 decimal places is 20.97617696340303093982907. Hence, the square root of 440 is an irrational number.

☛ Also Check:

Square Root of 80 - √80 = 8.94427
Square Root of 34 - √34 = 5.83095
Square Root of 320 - √320 = 17.88854
Square Root of 27 - √27 = 5.19615
Square Root of 1681 - √1681 = 41
Square Root of 44 - √44 = 6.63325
Square Root of 89 - √89 = 9.43398

Square Root of 440 Solved Examples

Example 1: Solve the equation x² − 440 = 0

Solution:

x² - 440 = 0 i.e. x² = 440
x = ±√440
Since the value of the square root of 440 is 20.976,
⇒ x = +√440 or -√440 = 20.976 or -20.976.
Example 2: If the surface area of a cube is 2640 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 2640 in²
⇒ a = ±√440 in
Since length can't be negative,
⇒ a = √440
We know that the square root of 440 is 20.976.
⇒ a = 20.976 in
Example 3: If the area of a circle is 440π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 440π in²
⇒ r = ±√440 in
Since radius can't be negative,
⇒ r = √440
The square root of 440 is 20.976.
⇒ r = 20.976 in

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FAQs on the Square Root of 440

What is the Value of the Square Root of 440?

The square root of 440 is 20.97617.

Why is the Square Root of 440 an Irrational Number?

Upon prime factorizing 440 i.e. 2³ × 5¹ × 11¹, 2 is in odd power. Therefore, the square root of 440 is irrational.

Evaluate 7 plus 12 square root 440

The given expression is 7 + 12 √440. We know that the square root of 440 is 20.976. Therefore, 7 + 12 √440 = 7 + 12 × 20.976 = 7 + 251.714 = 258.714

What is the Square of the Square Root of 440?

The square of the square root of 440 is the number 440 itself i.e. (√440)² = (440)^2/2 = 440.

If the Square Root of 440 is 20.976. Find the Value of the Square Root of 4.4.

Let us represent √4.4 in p/q form i.e. √(440/100) = 4.4/10 = 2.098. Hence, the value of √4.4 = 2.098

What is the Square Root of -440?

The square root of -440 is an imaginary number. It can be written as √-440 = √-1 × √440 = i √440 = 20.976i
where i = √-1 and it is called the imaginary unit.

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