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Square Root of 778

The square root of 778 is expressed as √778 in the radical form and as (778)^½ or (778)^0.5 in the exponent form. The square root of 778 rounded up to 5 decimal places is 27.89265. It is the positive solution of the equation x² = 778.

Square Root of 778: 27.892651361962706
Square Root of 778 in exponential form: (778)^½ or (778)^0.5
Square Root of 778 in radical form: √778

Square Root of 778

1.	What is the Square Root of 778?
2.	How to find the Square Root of 778?
3.	Is the Square Root of 778 Irrational?
4.	FAQs

What is the Square Root of 778?

The square root of 778, (or root 778), is the number which when multiplied by itself gives the product as 778. Therefore, the square root of 778 = √778 = 27.892651361962706.

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How to Find Square Root of 778?

Square Root of 778 by Long Division Method

Value of √778 by Long Division Method

Explanation:

Forming pairs: 07 and 78
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 78, to the right of the remainder 3. The new dividend is now 378.
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 <= 378. After finding Z, together 4 and Z (7) form a new divisor 47 for the new dividend 378.
Divide 378 by 47 with the quotient as 7, giving the remainder = 378 - 47 × 7 = 378 - 329 = 49.
Now, let's find the decimal places after the quotient 27.
Bring down 00 to the right of this remainder 49. The new dividend is now 4900.
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 <= 4900. Together they form a new divisor (548) for the new dividend (4900).
Divide 4900 by 548 with the quotient as 8, giving the remainder = 4900 - 548 × 8 = 4900 - 4384 = 516.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 778.

Therefore, the square root of 778 by long division method is 27.8 approximately.

Is Square Root of 778 Irrational?

The actual value of √778 is undetermined. The value of √778 up to 25 decimal places is 27.89265136196270603649326. Hence, the square root of 778 is an irrational number.

☛ Also Check:

Square Root of 108 - √108 = 10.39230
Square Root of 56 - √56 = 7.48331
Square Root of 729 - √729 = 27
Square Root of 35 - √35 = 5.91608
Square Root of 60 - √60 = 7.74597
Square Root of 17 - √17 = 4.12311
Square Root of 320 - √320 = 17.88854

Square Root of 778 Solved Examples

Example 1: Solve the equation x² − 778 = 0

Solution:

x² - 778 = 0 i.e. x² = 778
x = ±√778
Since the value of the square root of 778 is 27.893,
⇒ x = +√778 or -√778 = 27.893 or -27.893.
Example 2: If the area of a circle is 778π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 778π in²
⇒ r = ±√778 in
Since radius can't be negative,
⇒ r = √778
The square root of 778 is 27.893.
⇒ r = 27.893 in
Example 3: If the area of a square is 778 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 = 778 in²
⇒ a = ±√778 in
Since length can't be negative,
⇒ a = √778 = 27.893 in

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FAQs on the Square Root of 778

What is the Value of the Square Root of 778?

The square root of 778 is 27.89265.

Why is the Square Root of 778 an Irrational Number?

Upon prime factorizing 778 i.e. 2¹ × 389¹, 2 is in odd power. Therefore, the square root of 778 is irrational.

What is the Value of 7 square root 778?

The square root of 778 is 27.893. Therefore, 7 √778 = 7 × 27.893 = 195.249.

If the Square Root of 778 is 27.893. Find the Value of the Square Root of 7.78.

Let us represent √7.78 in p/q form i.e. √(778/100) = 7.78/10 = 2.789. Hence, the value of √7.78 = 2.789

Evaluate 17 plus 10 square root 778

The given expression is 17 + 10 √778. We know that the square root of 778 is 27.893. Therefore, 17 + 10 √778 = 17 + 10 × 27.893 = 17 + 278.927 = 295.927

What is the Square Root of -778?

The square root of -778 is an imaginary number. It can be written as √-778 = √-1 × √778 = i √778 = 27.892i
where i = √-1 and it is called the imaginary unit.

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