Question

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

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

Explanation:

planation:

Step1: Simplify \(4\sqrt{24}\)

Factor 24 into \(4\times6\), so \(\sqrt{24}=\sqrt{4\times6}\). Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we get \(\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}\). Then \(4\sqrt{24}=4\times2\sqrt{6}=8\sqrt{6}\).

Step2: Simplify \(5\sqrt{54}\)

Factor 54 into \(9\times6\), so \(\sqrt{54}=\sqrt{9\times6}=\sqrt{9}\times\sqrt{6}=3\sqrt{6}\). Then \(5\sqrt{54}=5\times3\sqrt{6}=15\sqrt{6}\).

Step3: Subtract the two simplified expressions

\(4\sqrt{24}-5\sqrt{54}=8\sqrt{6}-15\sqrt{6}\). Combining like terms (since both terms have \(\sqrt{6}\)), we get \((8 - 15)\sqrt{6}=-7\sqrt{6}\).

Answer:

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