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Square Root of 776

The square root of 776 is expressed as √776 in the radical form and as (776)^½ or (776)^0.5 in the exponent form. The square root of 776 rounded up to 8 decimal places is 27.85677655. It is the positive solution of the equation x² = 776. We can express the square root of 776 in its lowest radical form as 2 √194.

Square Root of 776: 27.85677655436824
Square Root of 776 in exponential form: (776)^½ or (776)^0.5
Square Root of 776 in radical form: √776 or 2 √194

Square Root of 776

1.	What is the Square Root of 776?
2.	How to find the Square Root of 776?
3.	Is the Square Root of 776 Irrational?
4.	FAQs

What is the Square Root of 776?

The square root of 776, (or root 776), is the number which when multiplied by itself gives the product as 776. Therefore, the square root of 776 = √776 = 2 √194 = 27.85677655436824.

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How to Find Square Root of 776?

Square Root of 776 by Long Division Method

Value of √776 by Long Division Method

Explanation:

Forming pairs: 07 and 76
Find a number Y (2) such that whose square is <= 7. Now divide 07 by 2 with quotient as 2.
Bring down the next pair 76, to the right of the remainder 3. The new dividend is now 376.
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 7) such that 4Z × Z <= 376. After finding Z, together 4 and Z (7) form a new divisor 47 for the new dividend 376.
Divide 376 by 47 with the quotient as 7, giving the remainder = 376 - 47 × 7 = 376 - 329 = 47.
Now, let's find the decimal places after the quotient 27.
Bring down 00 to the right of this remainder 47. The new dividend is now 4700.
Add the last digit of quotient to divisor i.e. 7 + 47 = 54. To the right of 54, find a digit Z (which is 8) such that 54Z × Z <= 4700. Together they form a new divisor (548) for the new dividend (4700).
Divide 4700 by 548 with the quotient as 8, giving the remainder = 4700 - 548 × 8 = 4700 - 4384 = 316.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 776.

Therefore, the square root of 776 by long division method is 27.8 approx.

Is Square Root of 776 Irrational?

The actual value of √776 is undetermined. The value of √776 up to 25 decimal places is 27.85677655436823867693548. Hence, the square root of 776 is an irrational number.

☛ Also Check:

Square Root of 113 - √113 = 10.63015
Square Root of 240 - √240 = 15.49193
Square Root of 68 - √68 = 8.24621
Square Root of 77 - √77 = 8.77496
Square Root of 85 - √85 = 9.21954
Square Root of 625 - √625 = 25
Square Root of 1024 - √1024 = 32

Square Root of 776 Solved Examples

Example 1: Solve the equation x² − 776 = 0

Solution:

x² - 776 = 0 i.e. x² = 776
x = ±√776
Since the value of the square root of 776 is 27.857,
⇒ x = +√776 or -√776 = 27.857 or -27.857.
Example 2: If the surface area of a cube is 4656 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 4656 in²
⇒ a = ±√776 in
Since length can't be negative,
⇒ a = √776
We know that the square root of 776 is 27.857.
⇒ a = 27.857 in
Example 3: If the area of an equilateral triangle is 776√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 = 776√3 in²
⇒ a = ±√3104 in
Since length can't be negative,
⇒ a = √3104 = 2 √776
We know that the square root of 776 is 27.857.
⇒ a = 55.714 in

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FAQs on the Square Root of 776

What is the Value of the Square Root of 776?

The square root of 776 is 27.85677.

Why is the Square Root of 776 an Irrational Number?

Upon prime factorizing 776 i.e. 2³ × 97¹, 2 is in odd power. Therefore, the square root of 776 is irrational.

What is the Square Root of -776?

The square root of -776 is an imaginary number. It can be written as √-776 = √-1 × √776 = i √776 = 27.856i
where i = √-1 and it is called the imaginary unit.

Evaluate 17 plus 18 square root 776

The given expression is 17 + 18 √776. We know that the square root of 776 is 27.857. Therefore, 17 + 18 √776 = 17 + 18 × 27.857 = 17 + 501.422 = 518.422

Is the number 776 a Perfect Square?

The prime factorization of 776 = 2³ × 97¹. Here, the prime factor 2 is not in the pair. Therefore, 776 is not a perfect square.

What is the Square of the Square Root of 776?

The square of the square root of 776 is the number 776 itself i.e. (√776)² = (776)^2/2 = 776.

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