Question

1. $3sqrt{2} + 6sqrt{18}$

a) $15sqrt{2}$
b) $-21sqrt{2}$
c) $9sqrt{2}$
d) $21sqrt{2}$

1. $-6sqrt{3x} - 4sqrt{3x}$

a) $-10sqrt{6x}$
b) $24sqrt{6x}$
c) $-2sqrt{3x}$
d) $-10sqrt{3x}$

Explanation:

Step1: Simplify \( 3\sqrt{2} + 6\sqrt{18} \)

First, simplify \( \sqrt{18} \). We know that \( 18 = 9\times2 \), so \( \sqrt{18}=\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2} \).

Step2: Substitute back into the expression

Now substitute \( \sqrt{18} = 3\sqrt{2} \) into the original expression: \( 3\sqrt{2}+6\times(3\sqrt{2}) \).

Step3: Perform the multiplication

Calculate \( 6\times3\sqrt{2}=18\sqrt{2} \).

Step4: Combine like terms

Now we have \( 3\sqrt{2}+18\sqrt{2} \). Since both terms have \( \sqrt{2} \), we can combine them: \( (3 + 18)\sqrt{2}=21\sqrt{2} \).

For problem 26:

Step1: Simplify \( -6\sqrt{3x}-4\sqrt{3x} \)

Both terms have \( \sqrt{3x} \), so we can combine the coefficients.

Step2: Combine the coefficients

The coefficients are -6 and -4. So, \( (-6-4)\sqrt{3x}=-10\sqrt{3x} \).

Answer:

1. D) \( 21\sqrt{2} \)
2. D) \( -10\sqrt{3x} \)