Question

simplifica el radical, déjalo en forma radical.
$8\sqrt{2} - 4\sqrt{2}$
○ 4
○ $8\sqrt{4}$
○ $4\sqrt{4}$
○ $4\sqrt{2}$
pregunta 13
felicity está haciendo un árbol de factores para el número 72.
factor tree image with 72 at top, layer 1: 6 and 12, layer 2: 2, 3 (for 6) and 6, 2 (for 12), layer 3: 2, 3 (for 6 from layer 2); $72 = 2\cdot3\cdot2\cdot3$
felicity cometió un error en seleccionar
terminar en seleccionar
el árbol de factores correcto o

Explanation:

First Problem (Simplify \( 8\sqrt{2} - 4\sqrt{2} \))

Step 1: Identify like radicals

Both terms have \( \sqrt{2} \), so we can factor it out.
\( 8\sqrt{2} - 4\sqrt{2} = (8 - 4)\sqrt{2} \)

Step 2: Subtract the coefficients

Calculate \( 8 - 4 = 4 \).
So, \( (8 - 4)\sqrt{2} = 4\sqrt{2} \)

Step 1: Analyze Layer 2

In Layer 2, the factor of 12 is split into 6 and 2. But 6 is not a prime number, so it should be split into prime factors (2 and 3) immediately, instead of leaving 6 as a non - prime factor in Layer 2. So Felicity made a mistake in Layer 2.

Step 2: Correct the factor tree

To correctly factor 72, we start with \( 72=8\times9 \) or \( 72 = 6\times12 \) (but when using 6×12, we should split 6 into 2×3 and 12 into 2×6, then 6 into 2×3). The correct prime factorization of 72 is \( 72=2\times2\times2\times3\times3 \) (or \( 2^{3}\times3^{2} \)).

Answer:

\( 4\sqrt{2} \) (corresponding to the option "4√2")

Second Problem (Factor Tree for 72)