Question

Eliot is simplifying a radical. His work is shown.



Which statement best applies to Eliot’s mathematical work?

The equality is incorrect or invalid.
Removing the 4 from under the radical in the second step is incorrect or invalid.
The work shown above is correct; however, may be simplified further.
The work shown above is correct, and may not be simplified further.

Answer 1

Removing the 4 from under the radical in the second step is incorrect or invalid.

You can only take a factor out of a square root by replacing it with its square root. For example,
sqrt(12) = sqrt(4·3) = sqrt(4)·sqrt(3) = 2·sqrt(3),
not 4·sqrt(3). Also note when taking square roots of perfect squares you must use the nonnegative root (sqrt(a^2)=|a|).