Question

$\sqrt{64} = \sqrt{4 \cdot 16}$
$\sqrt{4 \cdot 16} = 2\sqrt{16}$
$\sqrt{64} = 2\sqrt{16}$
which statement best applies to eliot’s mathematical work?
the equality $\sqrt{64} = \sqrt{4 \cdot 16}$ is incorrect or invalid.
the work shown by eliot is correct; however, $2\sqrt{16}$ may be simplified further.

Explanation:

Step1: Verify first equality

Left side: $\sqrt{64}=8$; Right side: $\sqrt{4 \cdot 16}=\sqrt{64}=8$. So $\sqrt{64}=\sqrt{4 \cdot 16}$ is valid.

Step2: Verify second equality

$\sqrt{4 \cdot 16}=\sqrt{4} \cdot \sqrt{16}=2\sqrt{16}$, which is correct.

Step3: Check simplification potential

$2\sqrt{16}=2 \times 4=8$, so $2\sqrt{16}$ can be simplified further.

Answer:

The work shown by Eliot is correct; however, $2\sqrt{16}$ may be simplified further.