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Square Root of 392

The square root of 392 is expressed as √392 in the radical form and as (392)^½ or (392)^0.5 in the exponent form. The square root of 392 rounded up to 5 decimal places is 19.79899. It is the positive solution of the equation x² = 392. We can express the square root of 392 in its lowest radical form as 14 √2.

Square Root of 392: 19.79898987322333
Square Root of 392 in exponential form: (392)^½ or (392)^0.5
Square Root of 392 in radical form: √392 or 14 √2

Square Root of 392

1.	What is the Square Root of 392?
2.	How to find the Square Root of 392?
3.	Is the Square Root of 392 Irrational?
4.	FAQs

What is the Square Root of 392?

The square root of 392, (or root 392), is the number which when multiplied by itself gives the product as 392. Therefore, the square root of 392 = √392 = 14 √2 = 19.79898987322333.

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How to Find Square Root of 392?

Square Root of 392 by Long Division Method

Value of √392 by Long Division Method

Explanation:

Forming pairs: 03 and 92
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 92, to the right of the remainder 2. The new dividend is now 292.
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 <= 292. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 292.
Divide 292 by 29 with the quotient as 9, giving the remainder = 292 - 29 × 9 = 292 - 261 = 31.
Now, let's find the decimal places after the quotient 19.
Bring down 00 to the right of this remainder 31. The new dividend is now 3100.
Add the last digit of quotient to divisor i.e. 9 + 29 = 38. To the right of 38, find a digit Z (which is 7) such that 38Z × Z <= 3100. Together they form a new divisor (387) for the new dividend (3100).
Divide 3100 by 387 with the quotient as 7, giving the remainder = 3100 - 387 × 7 = 3100 - 2709 = 391.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 392.

Therefore, the square root of 392 by long division method is 19.7 approx.

Is Square Root of 392 Irrational?

The actual value of √392 is undetermined. The value of √392 up to 25 decimal places is 19.79898987322333068322364. Hence, the square root of 392 is an irrational number.

☛ Also Check:

Square Root of 28 - √28 = 5.29150
Square Root of 11 - √11 = 3.31662
Square Root of 50 - √50 = 7.07107
Square Root of 288 - √288 = 16.97056
Square Root of 14 - √14 = 3.74166
Square Root of 51 - √51 = 7.14143
Square Root of 29 - √29 = 5.38516

Square Root of 392 Solved Examples

Example 1: Solve the equation x² − 392 = 0

Solution:

x² - 392 = 0 i.e. x² = 392
x = ±√392
Since the value of the square root of 392 is 19.799,
⇒ x = +√392 or -√392 = 19.799 or -19.799.
Example 2: If the area of an equilateral triangle is 392√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 = 392√3 in²
⇒ a = ±√1568 in
Since length can't be negative,
⇒ a = √1568 = 2 √392
We know that the square root of 392 is 19.799.
⇒ a = 39.598 in
Example 3: If the surface area of a sphere is 1568π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1568π in²
⇒ r = ±√392 in
Since radius can't be negative,
⇒ r = √392
The square root of 392 is 19.799.
⇒ r = 19.799 in

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FAQs on the Square Root of 392

What is the Value of the Square Root of 392?

The square root of 392 is 19.79898.

Why is the Square Root of 392 an Irrational Number?

Upon prime factorizing 392 i.e. 2³ × 7², 2 is in odd power. Therefore, the square root of 392 is irrational.

What is the Square of the Square Root of 392?

The square of the square root of 392 is the number 392 itself i.e. (√392)² = (392)^2/2 = 392.

Evaluate 19 plus 13 square root 392

The given expression is 19 + 13 √392. We know that the square root of 392 is 19.799. Therefore, 19 + 13 √392 = 19 + 13 × 19.799 = 19 + 257.387 = 276.387

What is the Square Root of 392 in Simplest Radical Form?

We need to express 392 as the product of its prime factors i.e. 392 = 2 × 2 × 2 × 7 × 7. Therefore, √392 = √2 × 2 × 2 × 7 × 7 = 14 √2. Thus, the square root of 392 in the lowest radical form is 14 √2.

Is the number 392 a Perfect Square?

The prime factorization of 392 = 2³ × 7². Here, the prime factor 2 is not in the pair. Therefore, 392 is not a perfect square.

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