Why is the square root of 64 only positive 8, not negative 8?

Question

If the square of -8 is also 64, why isn't the square root of 64 also -8?

Answer 1

By convention.  -8 is also a valid square root of 64, and when you're solving an equation like x² = 64, there will be two solutions for that reason.  But when you're asked for 'the' square root of a number, the positive one is what they mean.

Answer 2

If a number is written without any sign what you assume its sign will be  ....yesss its assumed to be positive only so if any thing written inside the symbol √  without any sign like   √64  what will you assume its sign should be.....but if you want to find the solutions of the equation x² = 64 then you will consider all the possible values whose square is 64 that is -8 and 8 

Answer 3

Here is a line from Wikipedia (which, everyone knows, is the authority on everything).

 

In mathematics, a square root of a number a is a number y such that y² = a, in other words, a number y whose square (the result of multiplying the number by itself, or y × y) is a.  For example, 4 and −4 are square roots of 16 because

4² = (−4)² = 16.