For the entire radical v90x^2 , state the restriction on the variable. Then express each as a mixed radical?

Question

I'm guessing that there is no restriction because the expression is positive? I'd appreciate any steps for clear understanding

 

Thanks in advance

Answer 1

    Assuming that the expression is sqrt(90 x²),

 

the usual  mixed radical form is   3 x sqrt(10)

 

For this form the restriction is x ≥ 0.          The entire and mixed expressions do not evaluate to the same value if  x is negative. 

 

However, we can also write the mixed radical as   3 |x| sqrt(10) .   Written this way there is no restriction.