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Square Root of 394

The square root of 394 is expressed as √394 in the radical form and as (394)^½ or (394)^0.5 in the exponent form. The square root of 394 rounded up to 8 decimal places is 19.84943324. It is the positive solution of the equation x² = 394.

Square Root of 394: 19.849433241279208
Square Root of 394 in exponential form: (394)^½ or (394)^0.5
Square Root of 394 in radical form: √394

Square Root of 394

1.	What is the Square Root of 394?
2.	How to find the Square Root of 394?
3.	Is the Square Root of 394 Irrational?
4.	FAQs

What is the Square Root of 394?

The square root of 394, (or root 394), is the number which when multiplied by itself gives the product as 394. Therefore, the square root of 394 = √394 = 19.849433241279208.

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How to Find Square Root of 394?

Square Root of 394 by Long Division Method

Value of √394 by Long Division Method

Explanation:

Forming pairs: 03 and 94
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 94, to the right of the remainder 2. The new dividend is now 294.
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 <= 294. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 294.
Divide 294 by 29 with the quotient as 9, giving the remainder = 294 - 29 × 9 = 294 - 261 = 33.
Now, let's find the decimal places after the quotient 19.
Bring down 00 to the right of this remainder 33. The new dividend is now 3300.
Add the last digit of quotient to divisor i.e. 9 + 29 = 38. To the right of 38, find a digit Z (which is 8) such that 38Z × Z <= 3300. Together they form a new divisor (388) for the new dividend (3300).
Divide 3300 by 388 with the quotient as 8, giving the remainder = 3300 - 388 × 8 = 3300 - 3104 = 196.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 394.

Therefore, the square root of 394 by long division method is 19.8 approximately.

Is Square Root of 394 Irrational?

The actual value of √394 is undetermined. The value of √394 up to 25 decimal places is 19.84943324127920786917047. Hence, the square root of 394 is an irrational number.

☛ Also Check:

Square Root of 65 - √65 = 8.06226
Square Root of 85 - √85 = 9.21954
Square Root of 10 - √10 = 3.16228
Square Root of 116 - √116 = 10.77033
Square Root of 35 - √35 = 5.91608
Square Root of 125 - √125 = 11.18034
Square Root of 21 - √21 = 4.58258

Square Root of 394 Solved Examples

Example 1: Solve the equation x² − 394 = 0

Solution:

x² - 394 = 0 i.e. x² = 394
x = ±√394
Since the value of the square root of 394 is 19.849,
⇒ x = +√394 or -√394 = 19.849 or -19.849.
Example 2: If the area of an equilateral triangle is 394√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 = 394√3 in²
⇒ a = ±√1576 in
Since length can't be negative,
⇒ a = √1576 = 2 √394
We know that the square root of 394 is 19.849.
⇒ a = 39.699 in
Example 3: If the area of a circle is 394π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 394π in²
⇒ r = ±√394 in
Since radius can't be negative,
⇒ r = √394
The square root of 394 is 19.849.
⇒ r = 19.849 in

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FAQs on the Square Root of 394

What is the Value of the Square Root of 394?

The square root of 394 is 19.84943.

Why is the Square Root of 394 an Irrational Number?

Upon prime factorizing 394 i.e. 2¹ × 197¹, 2 is in odd power. Therefore, the square root of 394 is irrational.

What is the Value of 5 square root 394?

The square root of 394 is 19.849. Therefore, 5 √394 = 5 × 19.849 = 99.247.

What is the Square of the Square Root of 394?

The square of the square root of 394 is the number 394 itself i.e. (√394)² = (394)^2/2 = 394.

If the Square Root of 394 is 19.849. Find the Value of the Square Root of 3.94.

Let us represent √3.94 in p/q form i.e. √(394/100) = 3.94/10 = 1.985. Hence, the value of √3.94 = 1.985

What is the Square Root of 394 in Simplest Radical Form?

We need to express 394 as the product of its prime factors i.e. 394 = 2 × 197. Therefore, as visible, the radical form of the square root of 394 cannot be simplified further. Therefore, the simplest radical form of the square root of 394 can be written as √394

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