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Square Root of 520

The square root of 520 is expressed as √520 in the radical form and as (520)^½ or (520)^0.5 in the exponent form. The square root of 520 rounded up to 8 decimal places is 22.80350850. It is the positive solution of the equation x² = 520. We can express the square root of 520 in its lowest radical form as 2 √130.

Square Root of 520: 22.80350850198276
Square Root of 520 in exponential form: (520)^½ or (520)^0.5
Square Root of 520 in radical form: √520 or 2 √130

Square Root of 520

1.	What is the Square Root of 520?
2.	How to find the Square Root of 520?
3.	Is the Square Root of 520 Irrational?
4.	FAQs

What is the Square Root of 520?

The square root of 520, (or root 520), is the number which when multiplied by itself gives the product as 520. Therefore, the square root of 520 = √520 = 2 √130 = 22.80350850198276.

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How to Find Square Root of 520?

Square Root of 520 by Long Division Method

Value of √520 by Long Division Method

Explanation:

Forming pairs: 05 and 20
Find a number Y (2) such that whose square is <= 5. Now divide 05 by 2 with quotient as 2.
Bring down the next pair 20, to the right of the remainder 1. The new dividend is now 120.
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 2) such that 4Z × Z <= 120. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 120.
Divide 120 by 42 with the quotient as 2, giving the remainder = 120 - 42 × 2 = 120 - 84 = 36.
Now, let's find the decimal places after the quotient 22.
Bring down 00 to the right of this remainder 36. The new dividend is now 3600.
Add the last digit of quotient to divisor i.e. 2 + 42 = 44. To the right of 44, find a digit Z (which is 8) such that 44Z × Z <= 3600. Together they form a new divisor (448) for the new dividend (3600).
Divide 3600 by 448 with the quotient as 8, giving the remainder = 3600 - 448 × 8 = 3600 - 3584 = 16.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 520.

Therefore, the square root of 520 by long division method is 22.8 approximately.

Is Square Root of 520 Irrational?

The actual value of √520 is undetermined. The value of √520 up to 25 decimal places is 22.80350850198275958272098. Hence, the square root of 520 is an irrational number.

☛ Also Check:

Square Root of 50 - √50 = 7.07107
Square Root of 72 - √72 = 8.48528
Square Root of 41 - √41 = 6.40312
Square Root of 200 - √200 = 14.14214
Square Root of 35 - √35 = 5.91608
Square Root of 39 - √39 = 6.24500
Square Root of 169 - √169 = 13

Square Root of 520 Solved Examples

Example 1: Solve the equation x² − 520 = 0

Solution:

x² - 520 = 0 i.e. x² = 520
x = ±√520
Since the value of the square root of 520 is 22.804,
⇒ x = +√520 or -√520 = 22.804 or -22.804.
Example 2: If the surface area of a cube is 3120 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 = 3120 in²
⇒ a = ±√520 in
Since length can't be negative,
⇒ a = √520
We know that the square root of 520 is 22.804.
⇒ a = 22.804 in
Example 3: If the area of a square is 520 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 = 520 in²
⇒ a = ±√520 in
Since length can't be negative,
⇒ a = √520 = 22.804 in

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FAQs on the Square Root of 520

What is the Value of the Square Root of 520?

The square root of 520 is 22.8035.

Why is the Square Root of 520 an Irrational Number?

Upon prime factorizing 520 i.e. 2³ × 5¹ × 13¹, 2 is in odd power. Therefore, the square root of 520 is irrational.

What is the Square of the Square Root of 520?

The square of the square root of 520 is the number 520 itself i.e. (√520)² = (520)^2/2 = 520.

What is the Square Root of -520?

The square root of -520 is an imaginary number. It can be written as √-520 = √-1 × √520 = i √520 = 22.803i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 520 in Simplest Radical Form?

We need to express 520 as the product of its prime factors i.e. 520 = 2 × 2 × 2 × 5 × 13. Therefore, √520 = √2 × 2 × 2 × 5 × 13 = 2 √130. Thus, the square root of 520 in the lowest radical form is 2 √130.

What is the Value of 1 square root 520?

The square root of 520 is 22.804. Therefore, 1 √520 = 1 × 22.804 = 22.804.

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