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

Square Root of 768

The square root of 768 is expressed as √768 in the radical form and as (768)^½ or (768)^0.5 in the exponent form. The square root of 768 rounded up to 9 decimal places is 27.712812921. It is the positive solution of the equation x² = 768. We can express the square root of 768 in its lowest radical form as 16 √3.

Square Root of 768: 27.712812921102035
Square Root of 768 in exponential form: (768)^½ or (768)^0.5
Square Root of 768 in radical form: √768 or 16 √3

Square Root of 768

1.	What is the Square Root of 768?
2.	How to find the Square Root of 768?
3.	Is the Square Root of 768 Irrational?
4.	FAQs

What is the Square Root of 768?

The square root of 768, (or root 768), is the number which when multiplied by itself gives the product as 768. Therefore, the square root of 768 = √768 = 16 √3 = 27.712812921102035.

☛ Check: Square Root Calculator

How to Find Square Root of 768?

Square Root of 768 by Long Division Method

Value of √768 by Long Division Method

Explanation:

Forming pairs: 07 and 68
Find a number Y (2) such that whose square is <= 7. Now divide 07 by 2 with quotient as 2.
Bring down the next pair 68, to the right of the remainder 3. The new dividend is now 368.
Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 7) such that 4Z × Z <= 368. After finding Z, together 4 and Z (7) form a new divisor 47 for the new dividend 368.
Divide 368 by 47 with the quotient as 7, giving the remainder = 368 - 47 × 7 = 368 - 329 = 39.
Now, let's find the decimal places after the quotient 27.
Bring down 00 to the right of this remainder 39. The new dividend is now 3900.
Add the last digit of quotient to divisor i.e. 7 + 47 = 54. To the right of 54, find a digit Z (which is 7) such that 54Z × Z <= 3900. Together they form a new divisor (547) for the new dividend (3900).
Divide 3900 by 547 with the quotient as 7, giving the remainder = 3900 - 547 × 7 = 3900 - 3829 = 71.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 768.

Therefore, the square root of 768 by long division method is 27.7 approximately.

Is Square Root of 768 Irrational?

The actual value of √768 is undetermined. The value of √768 up to 25 decimal places is 27.71281292110203669643914. Hence, the square root of 768 is an irrational number.

☛ Also Check:

Square Root of 68 - √68 = 8.24621
Square Root of 75 - √75 = 8.66025
Square Root of 41 - √41 = 6.40312
Square Root of 1024 - √1024 = 32
Square Root of 39 - √39 = 6.24500
Square Root of 400 - √400 = 20
Square Root of 73 - √73 = 8.54400

Square Root of 768 Solved Examples

Example 1: Solve the equation x² − 768 = 0

Solution:

x² - 768 = 0 i.e. x² = 768
x = ±√768
Since the value of the square root of 768 is 27.713,
⇒ x = +√768 or -√768 = 27.713 or -27.713.
Example 2: If the surface area of a sphere is 3072π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 3072π in²
⇒ r = ±√768 in
Since radius can't be negative,
⇒ r = √768
The square root of 768 is 27.713.
⇒ r = 27.713 in
Example 3: If the surface area of a cube is 4608 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 = 4608 in²
⇒ a = ±√768 in
Since length can't be negative,
⇒ a = √768
We know that the square root of 768 is 27.713.
⇒ a = 27.713 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 768

What is the Value of the Square Root of 768?

The square root of 768 is 27.71281.

Why is the Square Root of 768 an Irrational Number?

Upon prime factorizing 768 i.e. 2⁸ × 3¹, 3 is in odd power. Therefore, the square root of 768 is irrational.

If the Square Root of 768 is 27.713. Find the Value of the Square Root of 7.68.

Let us represent √7.68 in p/q form i.e. √(768/100) = 7.68/10 = 2.771. Hence, the value of √7.68 = 2.771

What is the Square of the Square Root of 768?

The square of the square root of 768 is the number 768 itself i.e. (√768)² = (768)^2/2 = 768.

What is the Square Root of 768 in Simplest Radical Form?

We need to express 768 as the product of its prime factors i.e. 768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3. Therefore, √768 = √2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 16 √3. Thus, the square root of 768 in the lowest radical form is 16 √3.

What is the Square Root of -768?

The square root of -768 is an imaginary number. It can be written as √-768 = √-1 × √768 = i √768 = 27.712i
where i = √-1 and it is called the imaginary unit.

Math worksheets and
visual curriculum