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Square Root of 3600

The square root of 3600 is expressed as √3600 in the radical form and as (3600)^½ or (3600)^0.5 in the exponent form. The square root of 3600 is 60. It is the positive solution of the equation x² = 3600. The number 3600 is a perfect square.

Square Root of 3600: 60
Square Root of 3600 in exponential form: (3600)^½ or (3600)^0.5
Square Root of 3600 in radical form: √3600

Square Root of 3600

1.	What is the Square Root of 3600?
2.	How to find the Square Root of 3600?
3.	Is the Square Root of 3600 Rational?
4.	FAQs

What is the Square Root of 3600?

The square root of 3600, (or root 3600), is the number which when multiplied by itself gives the product as 3600. Therefore, the square root of 3600 = √3600 = 60.

☛ Check: Square Root Calculator

How to Find Square Root of 3600?

Square Root of 3600 by Long Division Method

Value of √3600 by Long Division Method

Explanation:

Forming pairs: 36 and 00
Find a number Y (6) such that whose square is <= 36. Now divide 36 by 6 with quotient as 6.
Bring down the next pair 00, to the right of the remainder 0. The new dividend is now 0.
Add the last digit of the quotient (6) to the divisor (6) i.e. 6 + 6 = 12. To the right of 12, find a digit Z (which is 0) such that 12Z × Z <= 0. After finding Z, together 12 and Z (0) form a new divisor 120 for the new dividend 0.
Divide 0 by 120 with the quotient as 0, giving the remainder = 0 - 120 × 0 = 0 - 0 = 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 3600 by long division method is 60.

Is Square Root of 3600 Rational?

The value of √3600 is 60. Hence, the square root of 3600 is a rational number.

☛ Also Check:

Square Root of 14 - √14 = 3.74166
Square Root of 240 - √240 = 15.49193
Square Root of 11 - √11 = 3.31662
Square Root of 69 - √69 = 8.30662
Square Root of 1024 - √1024 = 32
Square Root of 42 - √42 = 6.48074
Square Root of 15 - √15 = 3.87298

Square Root of 3600 Solved Examples

Example 1: Solve the equation x² − 3600 = 0

Solution:

x² - 3600 = 0 i.e. x² = 3600
x = ±√3600
Since the value of the square root of 3600 is 60,
⇒ x = +√3600 or -√3600 = 60 or -60.
Example 2: If the area of a square is 3600 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 = 3600 in²
⇒ a = ±√3600 in
Since length can't be negative,
⇒ a = √3600 = 60 in
Example 3: If the area of an equilateral triangle is 3600√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 3600√3 in²
⇒ a = ±√14400 in
Since length can't be negative,
⇒ a = √14400 = 2 √3600
We know that the square root of 3600 is 60.
⇒ a = 120 in

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FAQs on the Square Root of 3600

What is the Value of the Square Root of 3600?

The square root of 3600 is 60.

Why is the Square Root of 3600 a Rational Number?

Upon prime factorizing 3600 i.e. 2⁴ × 3² × 5², we find that all the prime factors are in even power. This implies that the square root of 3600 is a positive integer. Therefore, the square root of 3600 is rational.

Evaluate 12 plus 13 square root 3600

The given expression is 12 + 13 √3600. We know that the square root of 3600 is 60. Therefore, 12 + 13 √3600 = 12 + 13 × 60 = 12 + 780 = 792

What is the Value of 1 square root 3600?

The square root of 3600 is 60. Therefore, 1 √3600 = 1 × 60 = 60.

What is the Square of the Square Root of 3600?

The square of the square root of 3600 is the number 3600 itself i.e. (√3600)² = (3600)^2/2 = 3600.

Is the number 3600 a Perfect Square?

The prime factorization of 3600 = 2⁴ × 3² × 5². Here, all the numbers are in the power of 2. This implies that the square root of 3600 is a positive integer. Therefore, 3600 is a perfect square.

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