A day full of math games & activities. Find one near you.

Square Root of 384

The square root of 384 is expressed as √384 in the radical form and as (384)^½ or (384)^0.5 in the exponent form. The square root of 384 rounded up to 5 decimal places is 19.59592. It is the positive solution of the equation x² = 384. We can express the square root of 384 in its lowest radical form as 8 √6.

Square Root of 384: 19.595917942265423
Square Root of 384 in exponential form: (384)^½ or (384)^0.5
Square Root of 384 in radical form: √384 or 8 √6

Square Root of 384

1.	What is the Square Root of 384?
2.	How to find the Square Root of 384?
3.	Is the Square Root of 384 Irrational?
4.	FAQs

What is the Square Root of 384?

The square root of 384, (or root 384), is the number which when multiplied by itself gives the product as 384. Therefore, the square root of 384 = √384 = 8 √6 = 19.595917942265423.

☛ Check: Square Root Calculator

How to Find Square Root of 384?

Square Root of 384 by Long Division Method

Value of √384 by Long Division Method

Explanation:

Forming pairs: 03 and 84
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 84, to the right of the remainder 2. The new dividend is now 284.
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 <= 284. After finding Z, together 2 and Z (9) form a new divisor 29 for the new dividend 284.
Divide 284 by 29 with the quotient as 9, giving the remainder = 284 - 29 × 9 = 284 - 261 = 23.
Now, let's find the decimal places after the quotient 19.
Bring down 00 to the right of this remainder 23. The new dividend is now 2300.
Add the last digit of quotient to divisor i.e. 9 + 29 = 38. To the right of 38, find a digit Z (which is 5) such that 38Z × Z <= 2300. Together they form a new divisor (385) for the new dividend (2300).
Divide 2300 by 385 with the quotient as 5, giving the remainder = 2300 - 385 × 5 = 2300 - 1925 = 375.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 384.

Therefore, the square root of 384 by long division method is 19.5 approximately.

Is Square Root of 384 Irrational?

The actual value of √384 is undetermined. The value of √384 up to 25 decimal places is 19.59591794226542478557827. Hence, the square root of 384 is an irrational number.

☛ Also Check:

Square Root of 512 - √512 = 22.62742
Square Root of 10 - √10 = 3.16228
Square Root of 33 - √33 = 5.74456
Square Root of 50 - √50 = 7.07107
Square Root of 40 - √40 = 6.32456
Square Root of 96 - √96 = 9.79796
Square Root of 784 - √784 = 28

Square Root of 384 Solved Examples

Example 1: Solve the equation x² − 384 = 0

Solution:

x² - 384 = 0 i.e. x² = 384
x = ±√384
Since the value of the square root of 384 is 19.596,
⇒ x = +√384 or -√384 = 19.596 or -19.596.
Example 2: If the surface area of a cube is 2304 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 = 2304 in²
⇒ a = ±√384 in
Since length can't be negative,
⇒ a = √384
We know that the square root of 384 is 19.596.
⇒ a = 19.596 in
Example 3: If the area of a square is 384 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 = 384 in²
⇒ a = ±√384 in
Since length can't be negative,
⇒ a = √384 = 19.596 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 384

What is the Value of the Square Root of 384?

The square root of 384 is 19.59591.

Why is the Square Root of 384 an Irrational Number?

Upon prime factorizing 384 i.e. 2⁷ × 3¹, 2 is in odd power. Therefore, the square root of 384 is irrational.

What is the Square of the Square Root of 384?

The square of the square root of 384 is the number 384 itself i.e. (√384)² = (384)^2/2 = 384.

What is the Value of 9 square root 384?

The square root of 384 is 19.596. Therefore, 9 √384 = 9 × 19.596 = 176.363.

What is the Square Root of -384?

The square root of -384 is an imaginary number. It can be written as √-384 = √-1 × √384 = i √384 = 19.595i
where i = √-1 and it is called the imaginary unit.

Evaluate 3 plus 15 square root 384

The given expression is 3 + 15 √384. We know that the square root of 384 is 19.596. Therefore, 3 + 15 √384 = 3 + 15 × 19.596 = 3 + 293.939 = 296.939

Math worksheets and
visual curriculum