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Square Root of 2704

The square root of 2704 is expressed as √2704 in the radical form and as (2704)^½ or (2704)^0.5 in the exponent form. The square root of 2704 is 52. It is the positive solution of the equation x² = 2704. The number 2704 is a perfect square.

Square Root of 2704: 52
Square Root of 2704 in exponential form: (2704)^½ or (2704)^0.5
Square Root of 2704 in radical form: √2704

Square Root of 2704

1.	What is the Square Root of 2704?
2.	How to find the Square Root of 2704?
3.	Is the Square Root of 2704 Rational?
4.	FAQs

What is the Square Root of 2704?

The square root of 2704, (or root 2704), is the number which when multiplied by itself gives the product as 2704. Therefore, the square root of 2704 = √2704 = 52.

☛ Check: Square Root Calculator

How to Find Square Root of 2704?

Square Root of 2704 by Long Division Method

Value of √2704 by Long Division Method

Explanation:

Forming pairs: 27 and 04
Find a number Y (5) such that whose square is <= 27. Now divide 27 by 5 with quotient as 5.
Bring down the next pair 04, to the right of the remainder 2. The new dividend is now 204.
Add the last digit of the quotient (5) to the divisor (5) i.e. 5 + 5 = 10. To the right of 10, find a digit Z (which is 2) such that 10Z × Z <= 204. After finding Z, together 10 and Z (2) form a new divisor 102 for the new dividend 204.
Divide 204 by 102 with the quotient as 2, giving the remainder = 204 - 102 × 2 = 204 - 204 = 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 2704 by long division method is 52.

Is Square Root of 2704 Rational?

The value of √2704 is 52. Hence, the square root of 2704 is a rational number.

☛ Also Check:

Square Root of 196 - √196 = 14
Square Root of 288 - √288 = 16.97056
Square Root of 320 - √320 = 17.88854
Square Root of 149 - √149 = 12.20656
Square Root of 48 - √48 = 6.92820
Square Root of 37 - √37 = 6.08276
Square Root of 361 - √361 = 19

Square Root of 2704 Solved Examples

Example 1: Solve the equation x² − 2704 = 0

Solution:

x² - 2704 = 0 i.e. x² = 2704
x = ±√2704
Since the value of the square root of 2704 is 52,
⇒ x = +√2704 or -√2704 = 52 or -52.
Example 2: If the surface area of a sphere is 10816π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 10816π in²
⇒ r = ±√2704 in
Since radius can't be negative,
⇒ r = √2704
The square root of 2704 is 52.
⇒ r = 52 in
Example 3: If the area of a square is 2704 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 = 2704 in²
⇒ a = ±√2704 in
Since length can't be negative,
⇒ a = √2704 = 52 in

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FAQs on the Square Root of 2704

What is the Value of the Square Root of 2704?

The square root of 2704 is 52.

Why is the Square Root of 2704 a Rational Number?

Upon prime factorizing 2704 i.e. 2⁴ × 13², we find that all the prime factors are in even power. This implies that the square root of 2704 is a positive integer. Therefore, the square root of 2704 is rational.

Is the number 2704 a Perfect Square?

The prime factorization of 2704 = 2⁴ × 13². Here, all the numbers are in the power of 2. This implies that the square root of 2704 is a positive integer. Therefore, 2704 is a perfect square.

If the Square Root of 2704 is 52. Find the Value of the Square Root of 27.04.

Let us represent √27.04 in p/q form i.e. √(2704/100) = 27.04/10 = 5. Hence, the value of √27.04 = 5

What is the Value of 20 square root 2704?

The square root of 2704 is 52. Therefore, 20 √2704 = 20 × 52 = 1040.

What is the Square of the Square Root of 2704?

The square of the square root of 2704 is the number 2704 itself i.e. (√2704)² = (2704)^2/2 = 2704.

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