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Square Root of 585

The square root of 585 is expressed as √585 in the radical form and as (585)^½ or (585)^0.5 in the exponent form. The square root of 585 rounded up to 9 decimal places is 24.186773245. It is the positive solution of the equation x² = 585. We can express the square root of 585 in its lowest radical form as 3 √65.

Square Root of 585: 24.186773244895647
Square Root of 585 in exponential form: (585)^½ or (585)^0.5
Square Root of 585 in radical form: √585 or 3 √65

Square Root of 585

1.	What is the Square Root of 585?
2.	How to find the Square Root of 585?
3.	Is the Square Root of 585 Irrational?
4.	FAQs

What is the Square Root of 585?

The square root of 585, (or root 585), is the number which when multiplied by itself gives the product as 585. Therefore, the square root of 585 = √585 = 3 √65 = 24.186773244895647.

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How to Find Square Root of 585?

Square Root of 585 by Long Division Method

Value of √585 by Long Division Method

Explanation:

Forming pairs: 05 and 85
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 85, to the right of the remainder 1. The new dividend is now 185.
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 4) such that 4Z × Z <= 185. After finding Z, together 4 and Z (4) form a new divisor 44 for the new dividend 185.
Divide 185 by 44 with the quotient as 4, giving the remainder = 185 - 44 × 4 = 185 - 176 = 9.
Now, let's find the decimal places after the quotient 24.
Bring down 00 to the right of this remainder 9. The new dividend is now 900.
Add the last digit of quotient to divisor i.e. 4 + 44 = 48. To the right of 48, find a digit Z (which is 1) such that 48Z × Z <= 900. Together they form a new divisor (481) for the new dividend (900).
Divide 900 by 481 with the quotient as 1, giving the remainder = 900 - 481 × 1 = 900 - 481 = 419.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 585.

Therefore, the square root of 585 by long division method is 24.1 approximately.

Is Square Root of 585 Irrational?

The actual value of √585 is undetermined. The value of √585 up to 25 decimal places is 24.18677324489564895709984. Hence, the square root of 585 is an irrational number.

☛ Also Check:

Square Root of 324 - √324 = 18
Square Root of 136 - √136 = 11.66190
Square Root of 75 - √75 = 8.66025
Square Root of 1296 - √1296 = 36
Square Root of 288 - √288 = 16.97056
Square Root of 100 - √100 = 10
Square Root of 289 - √289 = 17

Square Root of 585 Solved Examples

Example 1: Solve the equation x² − 585 = 0

Solution:

x² - 585 = 0 i.e. x² = 585
x = ±√585
Since the value of the square root of 585 is 24.187,
⇒ x = +√585 or -√585 = 24.187 or -24.187.
Example 2: If the surface area of a sphere is 2340π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2340π in²
⇒ r = ±√585 in
Since radius can't be negative,
⇒ r = √585
The square root of 585 is 24.187.
⇒ r = 24.187 in
Example 3: If the area of a circle is 585π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 585π in²
⇒ r = ±√585 in
Since radius can't be negative,
⇒ r = √585
The square root of 585 is 24.187.
⇒ r = 24.187 in

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FAQs on the Square Root of 585

What is the Value of the Square Root of 585?

The square root of 585 is 24.18677.

Why is the Square Root of 585 an Irrational Number?

Upon prime factorizing 585 i.e. 3² × 5¹ × 13¹, 5 is in odd power. Therefore, the square root of 585 is irrational.

Is the number 585 a Perfect Square?

The prime factorization of 585 = 3² × 5¹ × 13¹. Here, the prime factor 5 is not in the pair. Therefore, 585 is not a perfect square.

Evaluate 8 plus 4 square root 585

The given expression is 8 + 4 √585. We know that the square root of 585 is 24.187. Therefore, 8 + 4 √585 = 8 + 4 × 24.187 = 8 + 96.747 = 104.747

What is the Square Root of 585 in Simplest Radical Form?

We need to express 585 as the product of its prime factors i.e. 585 = 3 × 3 × 5 × 13. Therefore, √585 = √3 × 3 × 5 × 13 = 3 √65. Thus, the square root of 585 in the lowest radical form is 3 √65.

What is the Square of the Square Root of 585?

The square of the square root of 585 is the number 585 itself i.e. (√585)² = (585)^2/2 = 585.

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