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Square Root of 1920

The square root of 1920 is expressed as √1920 in the radical form and as (1920)^½ or (1920)^0.5 in the exponent form. The square root of 1920 rounded up to 10 decimal places is 43.8178046004. It is the positive solution of the equation x² = 1920. We can express the square root of 1920 in its lowest radical form as 8 √30.

Square Root of 1920: 43.81780460041329
Square Root of 1920 in exponential form: (1920)^½ or (1920)^0.5
Square Root of 1920 in radical form: √1920 or 8 √30

Square Root of 1920

1.	What is the Square Root of 1920?
2.	How to find the Square Root of 1920?
3.	Is the Square Root of 1920 Irrational?
4.	FAQs

What is the Square Root of 1920?

The square root of 1920, (or root 1920), is the number which when multiplied by itself gives the product as 1920. Therefore, the square root of 1920 = √1920 = 8 √30 = 43.81780460041329.

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How to Find Square Root of 1920?

Square Root of 1920 by Long Division Method

Value of √1920 by Long Division Method

Explanation:

Forming pairs: 19 and 20
Find a number Y (4) such that whose square is <= 19. Now divide 19 by 4 with quotient as 4.
Bring down the next pair 20, to the right of the remainder 3. The new dividend is now 320.
Add the last digit of the quotient (4) to the divisor (4) i.e. 4 + 4 = 8. To the right of 8, find a digit Z (which is 3) such that 8Z × Z <= 320. After finding Z, together 8 and Z (3) form a new divisor 83 for the new dividend 320.
Divide 320 by 83 with the quotient as 3, giving the remainder = 320 - 83 × 3 = 320 - 249 = 71.
Now, let's find the decimal places after the quotient 43.
Bring down 00 to the right of this remainder 71. The new dividend is now 7100.
Add the last digit of quotient to divisor i.e. 3 + 83 = 86. To the right of 86, find a digit Z (which is 8) such that 86Z × Z <= 7100. Together they form a new divisor (868) for the new dividend (7100).
Divide 7100 by 868 with the quotient as 8, giving the remainder = 7100 - 868 × 8 = 7100 - 6944 = 156.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1920.

Therefore, the square root of 1920 by long division method is 43.8 approximately.

Is Square Root of 1920 Irrational?

The actual value of √1920 is undetermined. The value of √1920 up to 25 decimal places is 43.81780460041328907655758. Hence, the square root of 1920 is an irrational number.

☛ Also Check:

Square Root of 61 - √61 = 7.81025
Square Root of 400 - √400 = 20
Square Root of 21 - √21 = 4.58258
Square Root of 109 - √109 = 10.44031
Square Root of 42 - √42 = 6.48074
Square Root of 2 - √2 = 1.41421
Square Root of 250 - √250 = 15.81139

Square Root of 1920 Solved Examples

Example 1: Solve the equation x² − 1920 = 0

Solution:

x² - 1920 = 0 i.e. x² = 1920
x = ±√1920
Since the value of the square root of 1920 is 43.818,
⇒ x = +√1920 or -√1920 = 43.818 or -43.818.
Example 2: If the surface area of a sphere is 7680π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 7680π in²
⇒ r = ±√1920 in
Since radius can't be negative,
⇒ r = √1920
The square root of 1920 is 43.818.
⇒ r = 43.818 in
Example 3: If the area of an equilateral triangle is 1920√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 = 1920√3 in²
⇒ a = ±√7680 in
Since length can't be negative,
⇒ a = √7680 = 2 √1920
We know that the square root of 1920 is 43.818.
⇒ a = 87.636 in

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FAQs on the Square Root of 1920

What is the Value of the Square Root of 1920?

The square root of 1920 is 43.8178.

Why is the Square Root of 1920 an Irrational Number?

Upon prime factorizing 1920 i.e. 2⁷ × 3¹ × 5¹, 2 is in odd power. Therefore, the square root of 1920 is irrational.

What is the Square Root of 1920 in Simplest Radical Form?

We need to express 1920 as the product of its prime factors i.e. 1920 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5. Therefore, √1920 = √2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 = 8 √30. Thus, the square root of 1920 in the lowest radical form is 8 √30.

What is the Square Root of -1920?

The square root of -1920 is an imaginary number. It can be written as √-1920 = √-1 × √1920 = i √1920 = 43.817i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 1920 is 43.818. Find the Value of the Square Root of 19.2.

Let us represent √19.2 in p/q form i.e. √(1920/100) = 19.2/10 = 4.382. Hence, the value of √19.2 = 4.382

What is the Value of 4 square root 1920?

The square root of 1920 is 43.818. Therefore, 4 √1920 = 4 × 43.818 = 175.271.

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