Square Root of 1256
The square root of 1256 is expressed as √1256 in the radical form and as (1256)^{½} or (1256)^{0.5} in the exponent form. The square root of 1256 rounded up to 8 decimal places is 35.44009029. It is the positive solution of the equation x^{2} = 1256. We can express the square root of 1256 in its lowest radical form as 2 √314.
 Square Root of 1256: 35.4400902933387
 Square Root of 1256 in exponential form: (1256)^{½} or (1256)^{0.5}
 Square Root of 1256 in radical form: √1256 or 2 √314
1.  What is the Square Root of 1256? 
2.  How to find the Square Root of 1256? 
3.  Is the Square Root of 1256 Irrational? 
4.  FAQs 
What is the Square Root of 1256?
The square root of 1256, (or root 1256), is the number which when multiplied by itself gives the product as 1256. Therefore, the square root of 1256 = √1256 = 2 √314 = 35.4400902933387.
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How to Find Square Root of 1256?
Value of √1256 by Long Division Method
Explanation:
 Forming pairs: 12 and 56
 Find a number Y (3) such that whose square is <= 12. Now divide 12 by 3 with quotient as 3.
 Bring down the next pair 56, to the right of the remainder 3. The new dividend is now 356.
 Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 5) such that 6Z × Z <= 356. After finding Z, together 6 and Z (5) form a new divisor 65 for the new dividend 356.
 Divide 356 by 65 with the quotient as 5, giving the remainder = 356  65 × 5 = 356  325 = 31.
 Now, let's find the decimal places after the quotient 35.
 Bring down 00 to the right of this remainder 31. The new dividend is now 3100.
 Add the last digit of quotient to divisor i.e. 5 + 65 = 70. To the right of 70, find a digit Z (which is 4) such that 70Z × Z <= 3100. Together they form a new divisor (704) for the new dividend (3100).
 Divide 3100 by 704 with the quotient as 4, giving the remainder = 3100  704 × 4 = 3100  2816 = 284.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1256.
Therefore, the square root of 1256 by long division method is 35.4 approximately.
Is Square Root of 1256 Irrational?
The actual value of √1256 is undetermined. The value of √1256 up to 25 decimal places is 35.44009029333870080398225. Hence, the square root of 1256 is an irrational number.
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 Square Root of 11  √11 = 3.31662
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 Square Root of 36  √36 = 6
 Square Root of 51  √51 = 7.14143
 Square Root of 37  √37 = 6.08276
 Square Root of 10  √10 = 3.16228
Square Root of 1256 Solved Examples

Example 1: Solve the equation x^{2} − 1256 = 0
Solution:
x^{2}  1256 = 0 i.e. x^{2} = 1256
x = ±√1256
Since the value of the square root of 1256 is 35.440,
⇒ x = +√1256 or √1256 = 35.440 or 35.440. 
Example 2: If the area of a square is 1256 in^{2}. 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 = a^{2} = 1256 in^{2}
⇒ a = ±√1256 in
Since length can't be negative,
⇒ a = √1256 = 35.440 in 
Example 3: If the surface area of a cube is 7536 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} = 7536 in^{2}
⇒ a = ±√1256 in
Since length can't be negative,
⇒ a = √1256
We know that the square root of 1256 is 35.440.
⇒ a = 35.440 in
FAQs on the Square Root of 1256
What is the Value of the Square Root of 1256?
The square root of 1256 is 35.44009.
Why is the Square Root of 1256 an Irrational Number?
Upon prime factorizing 1256 i.e. 2^{3} × 157^{1}, 2 is in odd power. Therefore, the square root of 1256 is irrational.
What is the Square of the Square Root of 1256?
The square of the square root of 1256 is the number 1256 itself i.e. (√1256)^{2} = (1256)^{2/2} = 1256.
What is the Square Root of 1256?
The square root of 1256 is an imaginary number. It can be written as √1256 = √1 × √1256 = i √1256 = 35.44i
where i = √1 and it is called the imaginary unit.
Is the number 1256 a Perfect Square?
The prime factorization of 1256 = 2^{3} × 157^{1}. Here, the prime factor 2 is not in the pair. Therefore, 1256 is not a perfect square.
Evaluate 17 plus 18 square root 1256
The given expression is 17 + 18 √1256. We know that the square root of 1256 is 35.440. Therefore, 17 + 18 √1256 = 17 + 18 × 35.440 = 17 + 637.922 = 654.922