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Square Root of 365

The square root of 365 is expressed as √365 in the radical form and as (365)^½ or (365)^0.5 in the exponent form. The square root of 365 rounded up to 7 decimal places is 19.1049732. It is the positive solution of the equation x² = 365.

Square Root of 365: 19.1049731745428
Square Root of 365 in exponential form: (365)^½ or (365)^0.5
Square Root of 365 in radical form: √365

Square Root of 365

1.	What is the Square Root of 365?
2.	How to find the Square Root of 365?
3.	Is the Square Root of 365 Irrational?
4.	FAQs

What is the Square Root of 365?

The square root of 365, (or root 365), is the number which when multiplied by itself gives the product as 365. Therefore, the square root of 365 = √365 = 19.1049731745428.

☛ Check: Square Root Calculator

How to Find Square Root of 365?

Square Root of 365 by Long Division Method

Value of √365 by Long Division Method

Explanation:

Forming pairs: 03 and 65
Find a number Y (1) such that whose square is <= 3. Now divide 03 by 1 with quotient as 1.
Bring down the next pair 65, to the right of the remainder 2. The new dividend is now 265.
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 9) such that 2Z × Z <= 265. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 265.
Divide 265 by 29 with the quotient as 9, giving the remainder = 265 - 29 × 9 = 265 - 261 = 4.
Now, let's find the decimal places after the quotient 19.
Bring down 00 to the right of this remainder 4. The new dividend is now 400.
Add the last digit of quotient to divisor i.e. 9 + 29 = 38. To the right of 38, find a digit Z (which is 1) such that 38Z × Z <= 400. Together they form a new divisor (381) for the new dividend (400).
Divide 400 by 381 with the quotient as 1, giving the remainder = 400 - 381 × 1 = 400 - 381 = 19.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 365.

Therefore, the square root of 365 by long division method is 19.1 approx.

Is Square Root of 365 Irrational?

The actual value of √365 is undetermined. The value of √365 up to 25 decimal places is 19.10497317454280017916830. Hence, the square root of 365 is an irrational number.

☛ Also Check:

Square Root of 26 - √26 = 5.09902
Square Root of 21 - √21 = 4.58258
Square Root of 17 - √17 = 4.12311
Square Root of 85 - √85 = 9.21954
Square Root of 34 - √34 = 5.83095
Square Root of 14 - √14 = 3.74166
Square Root of 16 - √16 = 4

Square Root of 365 Solved Examples

Example 1: Solve the equation x² − 365 = 0

Solution:

x² - 365 = 0 i.e. x² = 365
x = ±√365
Since the value of the square root of 365 is 19.105,
⇒ x = +√365 or -√365 = 19.105 or -19.105.
Example 2: If the area of a square is 365 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 = 365 in²
⇒ a = ±√365 in
Since length can't be negative,
⇒ a = √365 = 19.105 in
Example 3: If the surface area of a cube is 2190 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 = 2190 in²
⇒ a = ±√365 in
Since length can't be negative,
⇒ a = √365
We know that the square root of 365 is 19.105.
⇒ a = 19.105 in

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FAQs on the Square Root of 365

What is the Value of the Square Root of 365?

The square root of 365 is 19.10497.

Why is the Square Root of 365 an Irrational Number?

Upon prime factorizing 365 i.e. 5¹ × 73¹, 5 is in odd power. Therefore, the square root of 365 is irrational.

What is the Square Root of 365 in Simplest Radical Form?

We need to express 365 as the product of its prime factors i.e. 365 = 5 × 73. Therefore, as visible, the radical form of the square root of 365 cannot be simplified further. Therefore, the simplest radical form of the square root of 365 can be written as √365

Is the number 365 a Perfect Square?

The prime factorization of 365 = 5¹ × 73¹. Here, the prime factor 5 is not in the pair. Therefore, 365 is not a perfect square.

What is the Value of 17 square root 365?

The square root of 365 is 19.105. Therefore, 17 √365 = 17 × 19.105 = 324.785.

If the Square Root of 365 is 19.105. Find the Value of the Square Root of 3.65.

Let us represent √3.65 in p/q form i.e. √(365/100) = 3.65/10 = 1.910. Hence, the value of √3.65 = 1.910

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