Square Root of 789
The square root of 789 is expressed as √789 in the radical form and as (789)^{½} or (789)^{0.5} in the exponent form. The square root of 789 rounded up to 10 decimal places is 28.0891438104. It is the positive solution of the equation x^{2} = 789.
 Square Root of 789: 28.089143810376278
 Square Root of 789 in exponential form: (789)^{½} or (789)^{0.5}
 Square Root of 789 in radical form: √789
1.  What is the Square Root of 789? 
2.  How to find the Square Root of 789? 
3.  Is the Square Root of 789 Irrational? 
4.  FAQs 
What is the Square Root of 789?
The square root of 789, (or root 789), is the number which when multiplied by itself gives the product as 789. Therefore, the square root of 789 = √789 = 28.089143810376278.
☛ Check: Square Root Calculator
How to Find Square Root of 789?
Value of √789 by Long Division Method
Explanation:
 Forming pairs: 07 and 89
 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 89, to the right of the remainder 3. The new dividend is now 389.
 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 8) such that 4Z × Z <= 389. After finding Z, together 4 and Z (8) form a new divisor 48 for the new dividend 389.
 Divide 389 by 48 with the quotient as 8, giving the remainder = 389  48 × 8 = 389  384 = 5.
 Now, let's find the decimal places after the quotient 28.
 Bring down 00 to the right of this remainder 5. The new dividend is now 500.
 Add the last digit of quotient to divisor i.e. 8 + 48 = 56. To the right of 56, find a digit Z (which is 0) such that 56Z × Z <= 500. Together they form a new divisor (560) for the new dividend (500).
 Divide 500 by 560 with the quotient as 0, giving the remainder = 500  560 × 0 = 500  0 = 500.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 789.
Therefore, the square root of 789 by long division method is 28.0 approximately.
Is Square Root of 789 Irrational?
The actual value of √789 is undetermined. The value of √789 up to 25 decimal places is 28.08914381037627853741012. Hence, the square root of 789 is an irrational number.
☛ Also Check:
 Square Root of 108  √108 = 10.39230
 Square Root of 39  √39 = 6.24500
 Square Root of 196  √196 = 14
 Square Root of 12  √12 = 3.46410
 Square Root of 10  √10 = 3.16228
 Square Root of 52  √52 = 7.21110
 Square Root of 51  √51 = 7.14143
Square Root of 789 Solved Examples

Example 1: Solve the equation x^{2} − 789 = 0
Solution:
x^{2}  789 = 0 i.e. x^{2} = 789
x = ±√789
Since the value of the square root of 789 is 28.089,
⇒ x = +√789 or √789 = 28.089 or 28.089. 
Example 2: If the area of an equilateral triangle is 789√3 in^{2}. 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)a^{2} = 789√3 in^{2}
⇒ a = ±√3156 in
Since length can't be negative,
⇒ a = √3156 = 2 √789
We know that the square root of 789 is 28.089.
⇒ a = 56.178 in 
Example 3: If the surface area of a cube is 4734 in^{2}. 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 = 6a^{2} = 4734 in^{2}
⇒ a = ±√789 in
Since length can't be negative,
⇒ a = √789
We know that the square root of 789 is 28.089.
⇒ a = 28.089 in
FAQs on the Square Root of 789
What is the Value of the Square Root of 789?
The square root of 789 is 28.08914.
Why is the Square Root of 789 an Irrational Number?
Upon prime factorizing 789 i.e. 3^{1} × 263^{1}, 3 is in odd power. Therefore, the square root of 789 is irrational.
What is the Square Root of 789 in Simplest Radical Form?
We need to express 789 as the product of its prime factors i.e. 789 = 3 × 263. Therefore, as visible, the radical form of the square root of 789 cannot be simplified further. Therefore, the simplest radical form of the square root of 789 can be written as √789
If the Square Root of 789 is 28.089. Find the Value of the Square Root of 7.89.
Let us represent √7.89 in p/q form i.e. √(789/100) = 7.89/10 = 2.809. Hence, the value of √7.89 = 2.809
What is the Square Root of 789?
The square root of 789 is an imaginary number. It can be written as √789 = √1 × √789 = i √789 = 28.089i
where i = √1 and it is called the imaginary unit.
Is the number 789 a Perfect Square?
The prime factorization of 789 = 3^{1} × 263^{1}. Here, the prime factor 3 is not in the pair. Therefore, 789 is not a perfect square.