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Square Root of 3640

The square root of 3640 is expressed as √3640 in the radical form and as (3640)^½ or (3640)^0.5 in the exponent form. The square root of 3640 rounded up to 7 decimal places is 60.3324125. It is the positive solution of the equation x² = 3640. We can express the square root of 3640 in its lowest radical form as 2 √910.

Square Root of 3640: 60.332412515993425
Square Root of 3640 in exponential form: (3640)^½ or (3640)^0.5
Square Root of 3640 in radical form: √3640 or 2 √910

Square Root of 3640

1.	What is the Square Root of 3640?
2.	How to find the Square Root of 3640?
3.	Is the Square Root of 3640 Irrational?
4.	FAQs

What is the Square Root of 3640?

The square root of 3640, (or root 3640), is the number which when multiplied by itself gives the product as 3640. Therefore, the square root of 3640 = √3640 = 2 √910 = 60.332412515993425.

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How to Find Square Root of 3640?

Square Root of 3640 by Long Division Method

Value of √3640 by Long Division Method

Explanation:

Forming pairs: 36 and 40
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 40, to the right of the remainder 0. The new dividend is now 40.
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 <= 40. After finding Z, together 12 and Z (0) form a new divisor 120 for the new dividend 40.
Divide 40 by 120 with the quotient as 0, giving the remainder = 40 - 120 × 0 = 40 - 0 = 40.
Now, let's find the decimal places after the quotient 60.
Bring down 00 to the right of this remainder 40. The new dividend is now 4000.
Add the last digit of quotient to divisor i.e. 0 + 120 = 120. To the right of 120, find a digit Z (which is 3) such that 120Z × Z <= 4000. Together they form a new divisor (1203) for the new dividend (4000).
Divide 4000 by 1203 with the quotient as 3, giving the remainder = 4000 - 1203 × 3 = 4000 - 3609 = 391.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 3640.

Therefore, the square root of 3640 by long division method is 60.3 approximately.

Is Square Root of 3640 Irrational?

The actual value of √3640 is undetermined. The value of √3640 up to 25 decimal places is 60.33241251599342434503353. Hence, the square root of 3640 is an irrational number.

☛ Also Check:

Square Root of 108 - √108 = 10.39230
Square Root of 80 - √80 = 8.94427
Square Root of 36 - √36 = 6
Square Root of 106 - √106 = 10.29563
Square Root of 125 - √125 = 11.18034
Square Root of 26 - √26 = 5.09902
Square Root of 50 - √50 = 7.07107

Square Root of 3640 Solved Examples

Example 1: Solve the equation x² − 3640 = 0

Solution:

x² - 3640 = 0 i.e. x² = 3640
x = ±√3640
Since the value of the square root of 3640 is 60.332,
⇒ x = +√3640 or -√3640 = 60.332 or -60.332.
Example 2: If the area of a square is 3640 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 = 3640 in²
⇒ a = ±√3640 in
Since length can't be negative,
⇒ a = √3640 = 60.332 in
Example 3: If the surface area of a sphere is 14560π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 14560π in²
⇒ r = ±√3640 in
Since radius can't be negative,
⇒ r = √3640
The square root of 3640 is 60.332.
⇒ r = 60.332 in

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FAQs on the Square Root of 3640

What is the Value of the Square Root of 3640?

The square root of 3640 is 60.33241.

Why is the Square Root of 3640 an Irrational Number?

Upon prime factorizing 3640 i.e. 2³ × 5¹ × 7¹ × 13¹, 2 is in odd power. Therefore, the square root of 3640 is irrational.

Evaluate 10 plus 16 square root 3640

The given expression is 10 + 16 √3640. We know that the square root of 3640 is 60.332. Therefore, 10 + 16 √3640 = 10 + 16 × 60.332 = 10 + 965.319 = 975.319

What is the Square Root of -3640?

The square root of -3640 is an imaginary number. It can be written as √-3640 = √-1 × √3640 = i √3640 = 60.332i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 3640 in Simplest Radical Form?

We need to express 3640 as the product of its prime factors i.e. 3640 = 2 × 2 × 2 × 5 × 7 × 13. Therefore, √3640 = √2 × 2 × 2 × 5 × 7 × 13 = 2 √910. Thus, the square root of 3640 in the lowest radical form is 2 √910.

Is the number 3640 a Perfect Square?

The prime factorization of 3640 = 2³ × 5¹ × 7¹ × 13¹. Here, the prime factor 2 is not in the pair. Therefore, 3640 is not a perfect square.

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