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Square Root of 389

The square root of 389 is expressed as √389 in the radical form and as (389)^½ or (389)^0.5 in the exponent form. The square root of 389 rounded up to 8 decimal places is 19.72308292. It is the positive solution of the equation x² = 389.

Square Root of 389: 19.72308292331602
Square Root of 389 in exponential form: (389)^½ or (389)^0.5
Square Root of 389 in radical form: √389

Square Root of 389

1.	What is the Square Root of 389?
2.	How to find the Square Root of 389?
3.	Is the Square Root of 389 Irrational?
4.	FAQs

What is the Square Root of 389?

The square root of 389, (or root 389), is the number which when multiplied by itself gives the product as 389. Therefore, the square root of 389 = √389 = 19.72308292331602.

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How to Find Square Root of 389?

Square Root of 389 by Long Division Method

Value of √389 by Long Division Method

Explanation:

Forming pairs: 03 and 89
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 89, to the right of the remainder 2. The new dividend is now 289.
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 <= 289. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 289.
Divide 289 by 29 with the quotient as 9, giving the remainder = 289 - 29 × 9 = 289 - 261 = 28.
Now, let's find the decimal places after the quotient 19.
Bring down 00 to the right of this remainder 28. The new dividend is now 2800.
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 <= 2800. Together they form a new divisor (387) for the new dividend (2800).
Divide 2800 by 387 with the quotient as 7, giving the remainder = 2800 - 387 × 7 = 2800 - 2709 = 91.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 389.

Therefore, the square root of 389 by long division method is 19.7 approx.

Is Square Root of 389 Irrational?

The actual value of √389 is undetermined. The value of √389 up to 25 decimal places is 19.72308292331601996806400. Hence, the square root of 389 is an irrational number.

☛ Also Check:

Square Root of 63 - √63 = 7.93725
Square Root of 2 - √2 = 1.41421
Square Root of 169 - √169 = 13
Square Root of 106 - √106 = 10.29563
Square Root of 512 - √512 = 22.62742
Square Root of 90 - √90 = 9.48683
Square Root of 108 - √108 = 10.39230

Square Root of 389 Solved Examples

Example 1: Solve the equation x² − 389 = 0

Solution:

x² - 389 = 0 i.e. x² = 389
x = ±√389
Since the value of the square root of 389 is 19.723,
⇒ x = +√389 or -√389 = 19.723 or -19.723.
Example 2: If the surface area of a sphere is 1556π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 1556π in²
⇒ r = ±√389 in
Since radius can't be negative,
⇒ r = √389
The square root of 389 is 19.723.
⇒ r = 19.723 in
Example 3: If the area of an equilateral triangle is 389√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 = 389√3 in²
⇒ a = ±√1556 in
Since length can't be negative,
⇒ a = √1556 = 2 √389
We know that the square root of 389 is 19.723.
⇒ a = 39.446 in

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FAQs on the Square Root of 389

What is the Value of the Square Root of 389?

The square root of 389 is 19.72308.

Why is the Square Root of 389 an Irrational Number?

The number 389 is prime. This implies that the number 389 is pairless and is not in the power of 2. Therefore, the square root of 389 is irrational.

Evaluate 9 plus 7 square root 389

The given expression is 9 + 7 √389. We know that the square root of 389 is 19.723. Therefore, 9 + 7 √389 = 9 + 7 × 19.723 = 9 + 138.062 = 147.062

What is the Value of 1 square root 389?

The square root of 389 is 19.723. Therefore, 1 √389 = 1 × 19.723 = 19.723.

What is the Square Root of -389?

The square root of -389 is an imaginary number. It can be written as √-389 = √-1 × √389 = i √389 = 19.723i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 389 is 19.723. Find the Value of the Square Root of 3.89.

Let us represent √3.89 in p/q form i.e. √(389/100) = 3.89/10 = 1.972. Hence, the value of √3.89 = 1.972

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