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Square Root of 864

The square root of 864 is expressed as √864 in the radical form and as (864)^½ or (864)^0.5 in the exponent form. The square root of 864 rounded up to 10 decimal places is 29.3938769134. It is the positive solution of the equation x² = 864. We can express the square root of 864 in its lowest radical form as 12 √6.

Square Root of 864: 29.393876913398138
Square Root of 864 in exponential form: (864)^½ or (864)^0.5
Square Root of 864 in radical form: √864 or 12 √6

Square Root of 864

1.	What is the Square Root of 864?
2.	How to find the Square Root of 864?
3.	Is the Square Root of 864 Irrational?
4.	FAQs

What is the Square Root of 864?

The square root of 864, (or root 864), is the number which when multiplied by itself gives the product as 864. Therefore, the square root of 864 = √864 = 12 √6 = 29.393876913398138.

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How to Find Square Root of 864?

Square Root of 864 by Long Division Method

Value of √864 by Long Division Method

Explanation:

Forming pairs: 08 and 64
Find a number Y (2) such that whose square is <= 8. Now divide 08 by 2 with quotient as 2.
Bring down the next pair 64, to the right of the remainder 4. The new dividend is now 464.
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 9) such that 4Z × Z <= 464. After finding Z, together 4 and Z (9) form a new divisor 49 for the new dividend 464.
Divide 464 by 49 with the quotient as 9, giving the remainder = 464 - 49 × 9 = 464 - 441 = 23.
Now, let's find the decimal places after the quotient 29.
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 + 49 = 58. To the right of 58, find a digit Z (which is 3) such that 58Z × Z <= 2300. Together they form a new divisor (583) for the new dividend (2300).
Divide 2300 by 583 with the quotient as 3, giving the remainder = 2300 - 583 × 3 = 2300 - 1749 = 551.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 864.

Therefore, the square root of 864 by long division method is 29.3 approximately.

Is Square Root of 864 Irrational?

The actual value of √864 is undetermined. The value of √864 up to 25 decimal places is 29.39387691339813717836741. Hence, the square root of 864 is an irrational number.

☛ Also Check:

Square Root of 400 - √400 = 20
Square Root of 325 - √325 = 18.02776
Square Root of 1296 - √1296 = 36
Square Root of 100 - √100 = 10
Square Root of 63 - √63 = 7.93725
Square Root of 65 - √65 = 8.06226
Square Root of 98 - √98 = 9.89949

Square Root of 864 Solved Examples

Example 1: Solve the equation x² − 864 = 0

Solution:

x² - 864 = 0 i.e. x² = 864
x = ±√864
Since the value of the square root of 864 is 29.394,
⇒ x = +√864 or -√864 = 29.394 or -29.394.
Example 2: If the surface area of a sphere is 3456π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 3456π in²
⇒ r = ±√864 in
Since radius can't be negative,
⇒ r = √864
The square root of 864 is 29.394.
⇒ r = 29.394 in
Example 3: If the area of a circle is 864π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 864π in²
⇒ r = ±√864 in
Since radius can't be negative,
⇒ r = √864
The square root of 864 is 29.394.
⇒ r = 29.394 in

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FAQs on the Square Root of 864

What is the Value of the Square Root of 864?

The square root of 864 is 29.39387.

Why is the Square Root of 864 an Irrational Number?

Upon prime factorizing 864 i.e. 2⁵ × 3³, 2 is in odd power. Therefore, the square root of 864 is irrational.

What is the Square Root of 864 in Simplest Radical Form?

We need to express 864 as the product of its prime factors i.e. 864 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. Therefore, √864 = √2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 12 √6. Thus, the square root of 864 in the lowest radical form is 12 √6.

If the Square Root of 864 is 29.394. Find the Value of the Square Root of 8.64.

Let us represent √8.64 in p/q form i.e. √(864/100) = 8.64/10 = 2.939. Hence, the value of √8.64 = 2.939

What is the Square of the Square Root of 864?

The square of the square root of 864 is the number 864 itself i.e. (√864)² = (864)^2/2 = 864.

What is the Value of 7 square root 864?

The square root of 864 is 29.394. Therefore, 7 √864 = 7 × 29.394 = 205.757.

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