The answer is 26.
The method for solving depends on the resources available and your mathematical ability.
With a computer or calculator, the solution is trivial.
You could try trial and improvement or, a more sophisticated way is the Newton Raphson method which will work for all kinds of roots.
Finally, there is a method that resembles long division that can be applied to square roots but I regret that I am not up to describing it through this browser.
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The square root of 676 is 26
What is a square root? Simply put, the square root of X2 is X, where X can be any number. Because 676=262 Therefore the square root of 676 is 26.
26 is be the square root of 676
26 * 26 = 676 and 676 / 26 = 26
26