Restriction on variables in these

3 square root of 3y^3

square root of 6x^2

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(a) Given the expression `3sqrt(3y^3)` :

In the real number system, an even root is defined for nonnegative numbers only. Thus in the reals, `3sqrt(3y^3)` is defined only if `3y^3>=0` .

`3y^3>=0 ==> y>=0`

So the restriction on the variable (the domain of the expression) is `y>=0` .

*** If you meant `root(3)(3y^3)` then there is no restriction in the real number system. We can always take the cube root (or any odd indexed root) of any number in the reals. ***

(b) Given `sqrt(6x^2)` : again in the real numbers the expression in the radicand must be nonnegative.

`6x^2>=0 ==> x>=0`

Then the restriction in the reals is `x>=0` .

*** In the complex numbers (a number system with the imaginary unit) there is no restriction. ***

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