Simplify [tex]10 \sqrt{3x} + 4 \sqrt{3x} + 5 \sqrt{3x}[/tex]

A. [tex]9 \sqrt{3x}[/tex]
B. [tex]9 \sqrt{6x}[/tex]
C. [tex]19 \sqrt{3x}[/tex]
D. [tex]19 \sqrt{9x^3}[/tex]



Answer :

To simplify the given expression [tex]\(10 \sqrt{3x} + 4 \sqrt{3x} + 5 \sqrt{3x}\)[/tex], follow these steps:

1. Identify Like Terms:
Notice that each term contains the same radical part, which is [tex]\(\sqrt{3x}\)[/tex].

2. Combine the Coefficients:
Since [tex]\(\sqrt{3x}\)[/tex] is a common factor in all terms, we can factor it out:
[tex]\[ 10 \sqrt{3x} + 4 \sqrt{3x} + 5 \sqrt{3x} = (10 + 4 + 5) \sqrt{3x} \][/tex]

3. Sum the Coefficients:
Add the coefficients [tex]\(10\)[/tex], [tex]\(4\)[/tex], and [tex]\(5\)[/tex]:
[tex]\[ 10 + 4 + 5 = 19 \][/tex]

4. Construct the Simplified Expression:
Multiply the sum of the coefficients by the common radical part:
[tex]\[ 19 \sqrt{3x} \][/tex]

Therefore, the simplified form of the given expression is:
[tex]\[ 19 \sqrt{3x} \][/tex]

The correct answer is:
[tex]\[ \boxed{19 \sqrt{3x}} \][/tex]