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Square Root of 205

The square root of 205 is expressed as √205 in the radical form and as (205)^½ or (205)^0.5 in the exponent form. The square root of 205 rounded up to 5 decimal places is 14.31782. It is the positive solution of the equation x² = 205.

Square Root of 205: 14.317821063276353
Square Root of 205 in exponential form: (205)^½ or (205)^0.5
Square Root of 205 in radical form: √205

Square Root of 205

1.	What is the Square Root of 205?
2.	How to find the Square Root of 205?
3.	Is the Square Root of 205 Irrational?
4.	FAQs

What is the Square Root of 205?

The square root of 205, (or root 205), is the number which when multiplied by itself gives the product as 205. Therefore, the square root of 205 = √205 = 14.317821063276353.

☛ Check: Square Root Calculator

How to Find Square Root of 205?

Square Root of 205 by Long Division Method

Value of √205 by Long Division Method

Explanation:

Forming pairs: 02 and 05
Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
Bring down the next pair 05, to the right of the remainder 1. The new dividend is now 105.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 4) such that 2Z × Z <= 105. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 105.
Divide 105 by 24 with the quotient as 4, giving the remainder = 105 - 24 × 4 = 105 - 96 = 9.
Now, let's find the decimal places after the quotient 14.
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 + 24 = 28. To the right of 28, find a digit Z (which is 3) such that 28Z × Z <= 900. Together they form a new divisor (283) for the new dividend (900).
Divide 900 by 283 with the quotient as 3, giving the remainder = 900 - 283 × 3 = 900 - 849 = 51.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 205.

Therefore, the square root of 205 by long division method is 14.3 approx.

Is Square Root of 205 Irrational?

The actual value of √205 is undetermined. The value of √205 up to 25 decimal places is 14.31782106327635315443960. Hence, the square root of 205 is an irrational number.

☛ Also Check:

Square Root of 19 - √19 = 4.35890
Square Root of 256 - √256 = 16
Square Root of 26 - √26 = 5.09902
Square Root of 49 - √49 = 7
Square Root of 729 - √729 = 27
Square Root of 676 - √676 = 26
Square Root of 100 - √100 = 10

Square Root of 205 Solved Examples

Example 1: Solve the equation x² − 205 = 0

Solution:

x² - 205 = 0 i.e. x² = 205
x = ±√205
Since the value of the square root of 205 is 14.318,
⇒ x = +√205 or -√205 = 14.318 or -14.318.
Example 2: If the area of a square is 205 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 = 205 in²
⇒ a = ±√205 in
Since length can't be negative,
⇒ a = √205 = 14.318 in
Example 3: If the surface area of a sphere is 820π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 820π in²
⇒ r = ±√205 in
Since radius can't be negative,
⇒ r = √205
The square root of 205 is 14.318.
⇒ r = 14.318 in

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FAQs on the Square Root of 205

What is the Value of the Square Root of 205?

The square root of 205 is 14.31782.

Why is the Square Root of 205 an Irrational Number?

Upon prime factorizing 205 i.e. 5¹ × 41¹, 5 is in odd power. Therefore, the square root of 205 is irrational.

What is the Square Root of 205 in Simplest Radical Form?

We need to express 205 as the product of its prime factors i.e. 205 = 5 × 41. Therefore, as visible, the radical form of the square root of 205 cannot be simplified further. Therefore, the simplest radical form of the square root of 205 can be written as √205

What is the Square Root of -205?

The square root of -205 is an imaginary number. It can be written as √-205 = √-1 × √205 = i √205 = 14.317i
where i = √-1 and it is called the imaginary unit.

Is the number 205 a Perfect Square?

The prime factorization of 205 = 5¹ × 41¹. Here, the prime factor 5 is not in the pair. Therefore, 205 is not a perfect square.

What is the Square of the Square Root of 205?

The square of the square root of 205 is the number 205 itself i.e. (√205)² = (205)^2/2 = 205.

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