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Square Root of 2304

The square root of 2304 is expressed as √2304 in the radical form and as (2304)^½ or (2304)^0.5 in the exponent form. The square root of 2304 is 48. It is the positive solution of the equation x² = 2304. The number 2304 is a perfect square.

Square Root of 2304: 48
Square Root of 2304 in exponential form: (2304)^½ or (2304)^0.5
Square Root of 2304 in radical form: √2304

Square Root of 2304

1.	What is the Square Root of 2304?
2.	How to find the Square Root of 2304?
3.	Is the Square Root of 2304 Rational?
4.	FAQs

What is the Square Root of 2304?

The square root of 2304, (or root 2304), is the number which when multiplied by itself gives the product as 2304. Therefore, the square root of 2304 = √2304 = 48.

☛ Check: Square Root Calculator

How to Find Square Root of 2304?

Square Root of 2304 by Long Division Method

Value of √2304 by Long Division Method

Explanation:

Forming pairs: 23 and 04
Find a number Y (4) such that whose square is <= 23. Now divide 23 by 4 with quotient as 4.
Bring down the next pair 04, to the right of the remainder 7. The new dividend is now 704.
Add the last digit of the quotient (4) to the divisor (4) i.e. 4 + 4 = 8. To the right of 8, find a digit Z (which is 8) such that 8Z × Z <= 704. After finding Z, together 8 and Z (8) form a new divisor 88 for the new dividend 704.
Divide 704 by 88 with the quotient as 8, giving the remainder = 704 - 88 × 8 = 704 - 704 = 0.
We stop the process since the remainder is now 0 and there are no more digits that can be brought down.

Therefore, the square root of 2304 by long division method is 48.

Is Square Root of 2304 Rational?

The value of √2304 is 48. Hence, the square root of 2304 is a rational number.

☛ Also Check:

Square Root of 136 - √136 = 11.66190
Square Root of 13 - √13 = 3.60555
Square Root of 40 - √40 = 6.32456
Square Root of 28 - √28 = 5.29150
Square Root of 900 - √900 = 30
Square Root of 1521 - √1521 = 39
Square Root of 289 - √289 = 17

Square Root of 2304 Solved Examples

Example 1: Solve the equation x² − 2304 = 0

Solution:

x² - 2304 = 0 i.e. x² = 2304
x = ±√2304
Since the value of the square root of 2304 is 48,
⇒ x = +√2304 or -√2304 = 48 or -48.
Example 2: If the surface area of a cube is 13824 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 = 13824 in²
⇒ a = ±√2304 in
Since length can't be negative,
⇒ a = √2304
We know that the square root of 2304 is 48.
⇒ a = 48 in
Example 3: If the area of a square is 2304 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 = 2304 in²
⇒ a = ±√2304 in
Since length can't be negative,
⇒ a = √2304 = 48 in

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FAQs on the Square Root of 2304

What is the Value of the Square Root of 2304?

The square root of 2304 is 48.

Why is the Square Root of 2304 a Rational Number?

Upon prime factorizing 2304 i.e. 2⁸ × 3², we find that all the prime factors are in even power. This implies that the square root of 2304 is a positive integer. Therefore, the square root of 2304 is rational.

What is the Square Root of -2304?

The square root of -2304 is an imaginary number. It can be written as √-2304 = √-1 × √2304 = i √2304 = 48i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 2304?

The square of the square root of 2304 is the number 2304 itself i.e. (√2304)² = (2304)^2/2 = 2304.

What is the Value of 16 square root 2304?

The square root of 2304 is 48. Therefore, 16 √2304 = 16 × 48 = 768.

If the Square Root of 2304 is 48. Find the Value of the Square Root of 23.04.

Let us represent √23.04 in p/q form i.e. √(2304/100) = 23.04/10 = 4. Hence, the value of √23.04 = 4

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