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Square Root of 666

The square root of 666 is expressed as √666 in the radical form and as (666)^½ or (666)^0.5 in the exponent form. The square root of 666 rounded up to 10 decimal places is 25.8069758011. It is the positive solution of the equation x² = 666. We can express the square root of 666 in its lowest radical form as 3 √74.

Square Root of 666: 25.80697580112788
Square Root of 666 in exponential form: (666)^½ or (666)^0.5
Square Root of 666 in radical form: √666 or 3 √74

Square Root of 666

1.	What is the Square Root of 666?
2.	How to find the Square Root of 666?
3.	Is the Square Root of 666 Irrational?
4.	FAQs

What is the Square Root of 666?

The square root of 666, (or root 666), is the number which when multiplied by itself gives the product as 666. Therefore, the square root of 666 = √666 = 3 √74 = 25.80697580112788.

☛ Check: Square Root Calculator

How to Find Square Root of 666?

Square Root of 666 by Long Division Method

Value of √666 by Long Division Method

Explanation:

Forming pairs: 06 and 66
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 66, to the right of the remainder 2. The new dividend is now 266.
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 5) such that 4Z × Z <= 266. After finding Z, together 4 and Z (5) form a new divisor 45 for the new dividend 266.
Divide 266 by 45 with the quotient as 5, giving the remainder = 266 - 45 × 5 = 266 - 225 = 41.
Now, let's find the decimal places after the quotient 25.
Bring down 00 to the right of this remainder 41. The new dividend is now 4100.
Add the last digit of quotient to divisor i.e. 5 + 45 = 50. To the right of 50, find a digit Z (which is 8) such that 50Z × Z <= 4100. Together they form a new divisor (508) for the new dividend (4100).
Divide 4100 by 508 with the quotient as 8, giving the remainder = 4100 - 508 × 8 = 4100 - 4064 = 36.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 666.

Therefore, the square root of 666 by long division method is 25.8 approx.

Is Square Root of 666 Irrational?

The actual value of √666 is undetermined. The value of √666 up to 25 decimal places is 25.80697580112788031518842. Hence, the square root of 666 is an irrational number.

☛ Also Check:

Square Root of 42 - √42 = 6.48074
Square Root of 256 - √256 = 16
Square Root of 99 - √99 = 9.94987
Square Root of 149 - √149 = 12.20656
Square Root of 225 - √225 = 15
Square Root of 19 - √19 = 4.35890
Square Root of 56 - √56 = 7.48331

Square Root of 666 Solved Examples

Example 1: Solve the equation x² − 666 = 0

Solution:

x² - 666 = 0 i.e. x² = 666
x = ±√666
Since the value of the square root of 666 is 25.807,
⇒ x = +√666 or -√666 = 25.807 or -25.807.
Example 2: If the area of an equilateral triangle is 666√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 = 666√3 in²
⇒ a = ±√2664 in
Since length can't be negative,
⇒ a = √2664 = 2 √666
We know that the square root of 666 is 25.807.
⇒ a = 51.614 in
Example 3: If the area of a square is 666 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 = 666 in²
⇒ a = ±√666 in
Since length can't be negative,
⇒ a = √666 = 25.807 in

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FAQs on the Square Root of 666

What is the Value of the Square Root of 666?

The square root of 666 is 25.80697.

Why is the Square Root of 666 an Irrational Number?

Upon prime factorizing 666 i.e. 2¹ × 3² × 37¹, 2 is in odd power. Therefore, the square root of 666 is irrational.

What is the Square of the Square Root of 666?

The square of the square root of 666 is the number 666 itself i.e. (√666)² = (666)^2/2 = 666.

What is the Square Root of -666?

The square root of -666 is an imaginary number. It can be written as √-666 = √-1 × √666 = i √666 = 25.806i
where i = √-1 and it is called the imaginary unit.

Evaluate 13 plus 16 square root 666

The given expression is 13 + 16 √666. We know that the square root of 666 is 25.807. Therefore, 13 + 16 √666 = 13 + 16 × 25.807 = 13 + 412.912 = 425.912

If the Square Root of 666 is 25.807. Find the Value of the Square Root of 6.66.

Let us represent √6.66 in p/q form i.e. √(666/100) = 6.66/10 = 2.581. Hence, the value of √6.66 = 2.581

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