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Square Root of 612

The square root of 612 is expressed as √612 in the radical form and as (612)^½ or (612)^0.5 in the exponent form. The square root of 612 rounded up to 6 decimal places is 24.738634. It is the positive solution of the equation x² = 612. We can express the square root of 612 in its lowest radical form as 6 √17.

Square Root of 612: 24.73863375370596
Square Root of 612 in exponential form: (612)^½ or (612)^0.5
Square Root of 612 in radical form: √612 or 6 √17

Square Root of 612

1.	What is the Square Root of 612?
2.	How to find the Square Root of 612?
3.	Is the Square Root of 612 Irrational?
4.	FAQs

What is the Square Root of 612?

The square root of 612, (or root 612), is the number which when multiplied by itself gives the product as 612. Therefore, the square root of 612 = √612 = 6 √17 = 24.73863375370596.

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How to Find Square Root of 612?

Square Root of 612 by Long Division Method

Value of √612 by Long Division Method

Explanation:

Forming pairs: 06 and 12
Find a number Y (2) such that whose square is <= 6. Now divide 06 by 2 with quotient as 2.
Bring down the next pair 12, to the right of the remainder 2. The new dividend is now 212.
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 4) such that 4Z × Z <= 212. After finding Z, together 4 and Z (4) form a new divisor 44 for the new dividend 212.
Divide 212 by 44 with the quotient as 4, giving the remainder = 212 - 44 × 4 = 212 - 176 = 36.
Now, let's find the decimal places after the quotient 24.
Bring down 00 to the right of this remainder 36. The new dividend is now 3600.
Add the last digit of quotient to divisor i.e. 4 + 44 = 48. To the right of 48, find a digit Z (which is 7) such that 48Z × Z <= 3600. Together they form a new divisor (487) for the new dividend (3600).
Divide 3600 by 487 with the quotient as 7, giving the remainder = 3600 - 487 × 7 = 3600 - 3409 = 191.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 612.

Therefore, the square root of 612 by long division method is 24.7 approximately.

Is Square Root of 612 Irrational?

The actual value of √612 is undetermined. The value of √612 up to 25 decimal places is 24.73863375370596329892846. Hence, the square root of 612 is an irrational number.

☛ Also Check:

Square Root of 325 - √325 = 18.02776
Square Root of 162 - √162 = 12.72792
Square Root of 625 - √625 = 25
Square Root of 240 - √240 = 15.49193
Square Root of 33 - √33 = 5.74456
Square Root of 41 - √41 = 6.40312
Square Root of 256 - √256 = 16

Square Root of 612 Solved Examples

Example 1: Solve the equation x² − 612 = 0

Solution:

x² - 612 = 0 i.e. x² = 612
x = ±√612
Since the value of the square root of 612 is 24.739,
⇒ x = +√612 or -√612 = 24.739 or -24.739.
Example 2: If the surface area of a sphere is 2448π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 2448π in²
⇒ r = ±√612 in
Since radius can't be negative,
⇒ r = √612
The square root of 612 is 24.739.
⇒ r = 24.739 in
Example 3: If the area of a square is 612 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 = 612 in²
⇒ a = ±√612 in
Since length can't be negative,
⇒ a = √612 = 24.739 in

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FAQs on the Square Root of 612

What is the Value of the Square Root of 612?

The square root of 612 is 24.73863.

Why is the Square Root of 612 an Irrational Number?

Upon prime factorizing 612 i.e. 2² × 3² × 17¹, 17 is in odd power. Therefore, the square root of 612 is irrational.

If the Square Root of 612 is 24.739. Find the Value of the Square Root of 6.12.

Let us represent √6.12 in p/q form i.e. √(612/100) = 6.12/10 = 2.474. Hence, the value of √6.12 = 2.474

What is the Square of the Square Root of 612?

The square of the square root of 612 is the number 612 itself i.e. (√612)² = (612)^2/2 = 612.

What is the Square Root of -612?

The square root of -612 is an imaginary number. It can be written as √-612 = √-1 × √612 = i √612 = 24.738i
where i = √-1 and it is called the imaginary unit.

Is the number 612 a Perfect Square?

The prime factorization of 612 = 2² × 3² × 17¹. Here, the prime factor 17 is not in the pair. Therefore, 612 is not a perfect square.

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