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Square Root of 363

The square root of 363 is expressed as √363 in the radical form and as (363)^½ or (363)^0.5 in the exponent form. The square root of 363 rounded up to 10 decimal places is 19.0525588833. It is the positive solution of the equation x² = 363. We can express the square root of 363 in its lowest radical form as 11 √3.

Square Root of 363: 19.05255888325765
Square Root of 363 in exponential form: (363)^½ or (363)^0.5
Square Root of 363 in radical form: √363 or 11 √3

Square Root of 363

1.	What is the Square Root of 363?
2.	How to find the Square Root of 363?
3.	Is the Square Root of 363 Irrational?
4.	FAQs

What is the Square Root of 363?

The square root of 363, (or root 363), is the number which when multiplied by itself gives the product as 363. Therefore, the square root of 363 = √363 = 11 √3 = 19.05255888325765.

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How to Find Square Root of 363?

Square Root of 363 by Long Division Method

Value of √363 by Long Division Method

Explanation:

Forming pairs: 03 and 63
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 63, to the right of the remainder 2. The new dividend is now 263.
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 <= 263. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 263.
Divide 263 by 29 with the quotient as 9, giving the remainder = 263 - 29 × 9 = 263 - 261 = 2.
Now, let's find the decimal places after the quotient 19.
Bring down 00 to the right of this remainder 2. The new dividend is now 200.
Add the last digit of quotient to divisor i.e. 9 + 29 = 38. To the right of 38, find a digit Z (which is 0) such that 38Z × Z <= 200. Together they form a new divisor (380) for the new dividend (200).
Divide 200 by 380 with the quotient as 0, giving the remainder = 200 - 380 × 0 = 200 - 0 = 200.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 363.

Therefore, the square root of 363 by long division method is 19.0 approximately.

Is Square Root of 363 Irrational?

The actual value of √363 is undetermined. The value of √363 up to 25 decimal places is 19.05255888325765022880191. Hence, the square root of 363 is an irrational number.

☛ Also Check:

Square Root of 325 - √325 = 18.02776
Square Root of 10 - √10 = 3.16228
Square Root of 56 - √56 = 7.48331
Square Root of 288 - √288 = 16.97056
Square Root of 98 - √98 = 9.89949
Square Root of 400 - √400 = 20
Square Root of 289 - √289 = 17

Square Root of 363 Solved Examples

Example 1: Solve the equation x² − 363 = 0

Solution:

x² - 363 = 0 i.e. x² = 363
x = ±√363
Since the value of the square root of 363 is 19.053,
⇒ x = +√363 or -√363 = 19.053 or -19.053.
Example 2: If the area of a square is 363 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 = 363 in²
⇒ a = ±√363 in
Since length can't be negative,
⇒ a = √363 = 19.053 in
Example 3: If the surface area of a cube is 2178 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 = 2178 in²
⇒ a = ±√363 in
Since length can't be negative,
⇒ a = √363
We know that the square root of 363 is 19.053.
⇒ a = 19.053 in

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FAQs on the Square Root of 363

What is the Value of the Square Root of 363?

The square root of 363 is 19.05255.

Why is the Square Root of 363 an Irrational Number?

Upon prime factorizing 363 i.e. 3¹ × 11², 3 is in odd power. Therefore, the square root of 363 is irrational.

What is the Square Root of -363?

The square root of -363 is an imaginary number. It can be written as √-363 = √-1 × √363 = i √363 = 19.052i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 363 in Simplest Radical Form?

We need to express 363 as the product of its prime factors i.e. 363 = 3 × 11 × 11. Therefore, √363 = √3 × 11 × 11 = 11 √3. Thus, the square root of 363 in the lowest radical form is 11 √3.

Evaluate 18 plus 18 square root 363

The given expression is 18 + 18 √363. We know that the square root of 363 is 19.053. Therefore, 18 + 18 √363 = 18 + 18 × 19.053 = 18 + 342.946 = 360.946

Is the number 363 a Perfect Square?

The prime factorization of 363 = 3¹ × 11². Here, the prime factor 3 is not in the pair. Therefore, 363 is not a perfect square.

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