Square Root of 2600
The square root of 2600 is expressed as √2600 in the radical form and as (2600)^{½} or (2600)^{0.5} in the exponent form. The square root of 2600 rounded up to 10 decimal places is 50.9901951359. It is the positive solution of the equation x^{2} = 2600. We can express the square root of 2600 in its lowest radical form as 10 √26.
 Square Root of 2600: 50.99019513592785
 Square Root of 2600 in exponential form: (2600)^{½} or (2600)^{0.5}
 Square Root of 2600 in radical form: √2600 or 10 √26
1.  What is the Square Root of 2600? 
2.  How to find the Square Root of 2600? 
3.  Is the Square Root of 2600 Irrational? 
4.  FAQs 
What is the Square Root of 2600?
The square root of 2600, (or root 2600), is the number which when multiplied by itself gives the product as 2600. Therefore, the square root of 2600 = √2600 = 10 √26 = 50.99019513592785.
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How to Find Square Root of 2600?
Value of √2600 by Long Division Method
Explanation:
 Forming pairs: 26 and 00
 Find a number Y (5) such that whose square is <= 26. Now divide 26 by 5 with quotient as 5.
 Bring down the next pair 00, to the right of the remainder 1. The new dividend is now 100.
 Add the last digit of the quotient (5) to the divisor (5) i.e. 5 + 5 = 10. To the right of 10, find a digit Z (which is 0) such that 10Z × Z <= 100. After finding Z, together 10 and Z (0) form a new divisor 100 for the new dividend 100.
 Divide 100 by 100 with the quotient as 0, giving the remainder = 100  100 × 0 = 100  0 = 100.
 Now, let's find the decimal places after the quotient 50.
 Bring down 00 to the right of this remainder 100. The new dividend is now 10000.
 Add the last digit of quotient to divisor i.e. 0 + 100 = 100. To the right of 100, find a digit Z (which is 9) such that 100Z × Z <= 10000. Together they form a new divisor (1009) for the new dividend (10000).
 Divide 10000 by 1009 with the quotient as 9, giving the remainder = 10000  1009 × 9 = 10000  9081 = 919.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 2600.
Therefore, the square root of 2600 by long division method is 50.9 approx.
Is Square Root of 2600 Irrational?
The actual value of √2600 is undetermined. The value of √2600 up to 25 decimal places is 50.99019513592784830028224. Hence, the square root of 2600 is an irrational number.
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Square Root of 2600 Solved Examples

Example 1: Solve the equation x^{2} − 2600 = 0
Solution:
x^{2}  2600 = 0 i.e. x^{2} = 2600
x = ±√2600
Since the value of the square root of 2600 is 50.990,
⇒ x = +√2600 or √2600 = 50.990 or 50.990. 
Example 2: If the surface area of a sphere is 10400π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 10400π in^{2}
⇒ r = ±√2600 in
Since radius can't be negative,
⇒ r = √2600
The square root of 2600 is 50.990.
⇒ r = 50.990 in 
Example 3: If the surface area of a cube is 15600 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} = 15600 in^{2}
⇒ a = ±√2600 in
Since length can't be negative,
⇒ a = √2600
We know that the square root of 2600 is 50.990.
⇒ a = 50.990 in
FAQs on the Square Root of 2600
What is the Value of the Square Root of 2600?
The square root of 2600 is 50.99019.
Why is the Square Root of 2600 an Irrational Number?
Upon prime factorizing 2600 i.e. 2^{3} × 5^{2} × 13^{1}, 2 is in odd power. Therefore, the square root of 2600 is irrational.
If the Square Root of 2600 is 50.990. Find the Value of the Square Root of 26.
Let us represent √26 in p/q form i.e. √(2600/100) = 26/10 = 5.099. Hence, the value of √26.0 = 5.099
What is the Square of the Square Root of 2600?
The square of the square root of 2600 is the number 2600 itself i.e. (√2600)^{2} = (2600)^{2/2} = 2600.
Is the number 2600 a Perfect Square?
The prime factorization of 2600 = 2^{3} × 5^{2} × 13^{1}. Here, the prime factor 2 is not in the pair. Therefore, 2600 is not a perfect square.
Evaluate 18 plus 10 square root 2600
The given expression is 18 + 10 √2600. We know that the square root of 2600 is 50.990. Therefore, 18 + 10 √2600 = 18 + 10 × 50.990 = 18 + 509.902 = 527.902