Question

3√18 - 2√2 =
a 6√3 - 2√2
b 7√2
c 11√2
d 18√3 - 2√2

Explanation:

Step1: Simplify \( 3\sqrt{18} \)

First, factor 18 into \( 9\times2 \). Then, \( \sqrt{18}=\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2} \) (since \( \sqrt{9} = 3 \)). So, \( 3\sqrt{18}=3\times3\sqrt{2}=9\sqrt{2} \).

Step2: Subtract \( 2\sqrt{2} \) from \( 9\sqrt{2} \)

Now we have the expression \( 9\sqrt{2}-2\sqrt{2} \). Since the terms have the same radical part (\( \sqrt{2} \)), we can combine them by subtracting the coefficients: \( (9 - 2)\sqrt{2}=7\sqrt{2} \)? Wait, no, wait. Wait, the original problem is \( 3\sqrt{18}-2\sqrt{2} \), but wait, maybe I misread. Wait, the user's problem: looking at the image, the problem is \( 3\sqrt{18}-2\sqrt{2} \)? Wait, no, the first part: maybe it's \( 3\sqrt{18} \) or is there a typo? Wait, no, let's re - check. Wait, the image shows the problem as \( 3\sqrt{18}-2\sqrt{2} \)? Wait, no, maybe the first term is \( 3\sqrt{18} \)? Wait, no, wait, the user's problem: let's see, the options: C is \( 11\sqrt{2} \), B is \( 7\sqrt{2} \). Wait, maybe the original problem is \( 3\sqrt{18}+ 2\sqrt{2} \)? No, the image says \( 3\sqrt{18}-2\sqrt{2} \)? Wait, no, maybe I made a mistake. Wait, \( \sqrt{18}=3\sqrt{2} \), so \( 3\sqrt{18}=3\times3\sqrt{2}=9\sqrt{2} \). Then \( 9\sqrt{2}-2\sqrt{2}=(9 - 2)\sqrt{2}=7\sqrt{2} \), but option C is \( 11\sqrt{2} \). Wait, maybe the problem is \( 3\sqrt{18}+8\sqrt{2}-2\sqrt{2} \)? No, the image: let's look again. The problem is \( 3\sqrt{18}-2\sqrt{2} \)? Wait, the options: A: \( 6\sqrt{3}-2\sqrt{2} \), B: \( 7\sqrt{2} \), C: \( 11\sqrt{2} \), D: \( 18\sqrt{3}-2\sqrt{2} \). Wait, maybe the original problem is \( 3\sqrt{18}+ 8\sqrt{2}-2\sqrt{2} \)? No, maybe I misread the coefficient. Wait, maybe the first term is \( 11\sqrt{18} \)? No, the image shows "3√18 - 2√2 =". Wait, maybe there's a mistake in my calculation. Wait, no, \( 3\sqrt{18}=3\times3\sqrt{2}=9\sqrt{2} \), \( 9\sqrt{2}-2\sqrt{2}=7\sqrt{2} \), which is option B. But the selected option is C. Wait, maybe the problem is \( 11\sqrt{18}-2\sqrt{2} \)? No, the image shows "3√18 - 2√2 =". Wait, maybe the user made a typo, but according to the calculation, \( 3\sqrt{18}-2\sqrt{2}=9\sqrt{2}-2\sqrt{2}=7\sqrt{2} \), which is option B. But the selected option in the image is C. Maybe there's a mistake in the problem statement. But according to the correct calculation:

Step1: Simplify \( \sqrt{18} \)

\( \sqrt{18}=\sqrt{9\times2}=3\sqrt{2} \)

Step2: Calculate \( 3\sqrt{18} \)

\( 3\sqrt{18}=3\times3\sqrt{2}=9\sqrt{2} \)

Step3: Subtract \( 2\sqrt{2} \)

\( 9\sqrt{2}-2\sqrt{2}=(9 - 2)\sqrt{2}=7\sqrt{2} \)

Answer:

B. \( 7\sqrt{2} \)