Is in ( square root x 2 exponent) = x an identity (true for all nonnegative values of x)?

Is in ( square root x 2 exponent) = x an identity (true for all nonnegative values of x)Is in ( square root x 2 exponent) = x an identity (true for all nonnegative values of x)?
This somewhat tricky. If you consider sqrt as a function, that is, the function that to each non-negative real number assigns it's positive square root, then the answer is sure yes. Simply because +sqrt(x^2) = x.





But if you think of sqrt as a relation, that is, as the number whose square is x, then you have 2 values for sqrt(x^2): x itself and also -x. Then, in this case the answer is no, not always.





But, by convention, when we just have sqrt(x), x%26gt;=0 real, it's understood the positive square root.Is in ( square root x 2 exponent) = x an identity (true for all nonnegative values of x)?
Yes, for all non-negative values of x, sqrt(x^2) = x
the square root of x to the second power is x. because it is the same as saying x to the power of 2/2. the cube root of x to the power of 3, will be x. any number rooted to the same power as the exponent of the base will leave you with just the base, but if the root number and the exponent are different then that's another story all together, for example, if you have the 7 root of x to the power of 4, it's the same as x to the 4/7 power. in that case, x will be taken to the power of 4, then rooted to the power of seven.