Question

what is the following difference?
11√45 − 4√5
options:
95√5
29√5
7√40
14√10

Explanation:

Step1: Simplify \( 11\sqrt{45} \)

Factor 45: \( 45 = 9 \times 5 \), so \( \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} \). Then \( 11\sqrt{45} = 11 \times 3\sqrt{5} = 33\sqrt{5} \).

Step2: Subtract \( 4\sqrt{5} \)

Now, \( 11\sqrt{45} - 4\sqrt{5} = 33\sqrt{5} - 4\sqrt{5} \). Combine like terms: \( (33 - 4)\sqrt{5} = 29\sqrt{5} \).

Answer:

\( 29\sqrt{5} \) (the option with \( 29\sqrt{5} \))