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Square Root of 504

The square root of 504 is expressed as √504 in the radical form and as (504)^½ or (504)^0.5 in the exponent form. The square root of 504 rounded up to 5 decimal places is 22.44994. It is the positive solution of the equation x² = 504. We can express the square root of 504 in its lowest radical form as 6 √14.

Square Root of 504: 22.44994432064365
Square Root of 504 in exponential form: (504)^½ or (504)^0.5
Square Root of 504 in radical form: √504 or 6 √14

Square Root of 504

1.	What is the Square Root of 504?
2.	How to find the Square Root of 504?
3.	Is the Square Root of 504 Irrational?
4.	FAQs

What is the Square Root of 504?

The square root of 504, (or root 504), is the number which when multiplied by itself gives the product as 504. Therefore, the square root of 504 = √504 = 6 √14 = 22.44994432064365.

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How to Find Square Root of 504?

Square Root of 504 by Long Division Method

Value of √504 by Long Division Method

Explanation:

Forming pairs: 05 and 04
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 04, to the right of the remainder 1. The new dividend is now 104.
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 <= 104. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 104.
Divide 104 by 42 with the quotient as 2, giving the remainder = 104 - 42 × 2 = 104 - 84 = 20.
Now, let's find the decimal places after the quotient 22.
Bring down 00 to the right of this remainder 20. The new dividend is now 2000.
Add the last digit of quotient to divisor i.e. 2 + 42 = 44. To the right of 44, find a digit Z (which is 4) such that 44Z × Z <= 2000. Together they form a new divisor (444) for the new dividend (2000).
Divide 2000 by 444 with the quotient as 4, giving the remainder = 2000 - 444 × 4 = 2000 - 1776 = 224.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 504.

Therefore, the square root of 504 by long division method is 22.4 approx.

Is Square Root of 504 Irrational?

The actual value of √504 is undetermined. The value of √504 up to 25 decimal places is 22.44994432064364831350249. Hence, the square root of 504 is an irrational number.

☛ Also Check:

Square Root of 39 - √39 = 6.24500
Square Root of 256 - √256 = 16
Square Root of 22 - √22 = 4.69042
Square Root of 200 - √200 = 14.14214
Square Root of 29 - √29 = 5.38516
Square Root of 900 - √900 = 30
Square Root of 76 - √76 = 8.71780

Square Root of 504 Solved Examples

Example 1: Solve the equation x² − 504 = 0

Solution:

x² - 504 = 0 i.e. x² = 504
x = ±√504
Since the value of the square root of 504 is 22.450,
⇒ x = +√504 or -√504 = 22.450 or -22.450.
Example 2: If the surface area of a cube is 3024 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 = 3024 in²
⇒ a = ±√504 in
Since length can't be negative,
⇒ a = √504
We know that the square root of 504 is 22.450.
⇒ a = 22.450 in
Example 3: If the area of an equilateral triangle is 504√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 = 504√3 in²
⇒ a = ±√2016 in
Since length can't be negative,
⇒ a = √2016 = 2 √504
We know that the square root of 504 is 22.450.
⇒ a = 44.900 in

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FAQs on the Square Root of 504

What is the Value of the Square Root of 504?

The square root of 504 is 22.44994.

Why is the Square Root of 504 an Irrational Number?

Upon prime factorizing 504 i.e. 2³ × 3² × 7¹, 2 is in odd power. Therefore, the square root of 504 is irrational.

If the Square Root of 504 is 22.450. Find the Value of the Square Root of 5.04.

Let us represent √5.04 in p/q form i.e. √(504/100) = 5.04/10 = 2.245. Hence, the value of √5.04 = 2.245

Is the number 504 a Perfect Square?

The prime factorization of 504 = 2³ × 3² × 7¹. Here, the prime factor 2 is not in the pair. Therefore, 504 is not a perfect square.

What is the Square Root of 504 in Simplest Radical Form?

We need to express 504 as the product of its prime factors i.e. 504 = 2 × 2 × 2 × 3 × 3 × 7. Therefore, √504 = √2 × 2 × 2 × 3 × 3 × 7 = 6 √14. Thus, the square root of 504 in the lowest radical form is 6 √14.

What is the Square of the Square Root of 504?

The square of the square root of 504 is the number 504 itself i.e. (√504)² = (504)^2/2 = 504.

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