`sqrt(9x^2)`
If x gt 0 , which of the following is equivalent to the given expression?

Options

A. 3x
B. `3x^2`
C. 18x
D. `18x^4`

Answer

A

Explanation

The expression `sqrt(9x^2)` can be rewritten as `(sqrt9)(sqt(x^2))` . The square root symbol in an expression represents the principal square root, or the positive square root, thus `sqrt9` = 3. Since x gt 0, taking the square root of the second factor, `sqrt(x^2)` , gives x. It follows that `sqrt(9x^2)` is equivalent to 3x.
Choice B is incorr_ect and may result from rewriting `sqrt(9x^2)` as `(sqrt9)(x^2)` rather than `(sqrt9)(sqrtx^2)`. Choices C and D are incorrect and may result from misunderstanding the operation indicated by a radical symbol. In both of these choices, instead of finding the square root of the coefficient 9, the coefficient has been multiplied by 2. Additionally, in choice D, `x^2` has been squared to give `x^4`, instead of taking the square root of `x^2` to get x.