Question

1. which of the following values is equal to $4sqrt{24} - 5sqrt{54}$?

a. $-29sqrt{6}$
b. $-7sqrt{6}$
c. $-2sqrt{6}$
d. $-sqrt{30}$
e. $-sqrt{1,296}$

Explanation:

Step1: Simplify \( \sqrt{24} \) and \( \sqrt{54} \)

Factor the radicands: \( 24 = 4\times6 \), \( 54 = 9\times6 \). So \( \sqrt{24}=\sqrt{4\times6}=2\sqrt{6} \), \( \sqrt{54}=\sqrt{9\times6}=3\sqrt{6} \).

Step2: Substitute into the expression

\( 4\sqrt{24}-5\sqrt{54}=4\times2\sqrt{6}-5\times3\sqrt{6} \).

Step3: Calculate the coefficients

\( 4\times2\sqrt{6}=8\sqrt{6} \), \( 5\times3\sqrt{6}=15\sqrt{6} \). Then \( 8\sqrt{6}-15\sqrt{6}=(8 - 15)\sqrt{6}=-7\sqrt{6} \).

Answer:

B. \( -7\sqrt{6} \)