Question

question 1-10
simplify. assume that all variables represent positive real numbers.
\\(\sqrt{4x} - 12\sqrt{3x} + 5\sqrt{9x}\\)
\\(\circ\\) \\(-7\sqrt{10x}\\)
\\(\circ\\) \\(-7\sqrt{16x}\\)
\\(\circ\\) \\(2\sqrt{x} + 3\sqrt{3x}\\)
\\(\circ\\) \\(17\sqrt{x} - 12\sqrt{3x}\\)

Explanation:

Step1: Simplify each square root term

We know that $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ (for $a\geq0,b\geq0$). So,

• For $\sqrt{4x}$, since $\sqrt{4x}=\sqrt{4}\cdot\sqrt{x}$ and $\sqrt{4} = 2$, we have $\sqrt{4x}=2\sqrt{x}$.
• For $5\sqrt{9x}$, since $\sqrt{9x}=\sqrt{9}\cdot\sqrt{x}$ and $\sqrt{9}=3$, we have $5\sqrt{9x}=5\times3\sqrt{x}=15\sqrt{x}$.

The original expression $\sqrt{4x}-12\sqrt{3x}+5\sqrt{9x}$ becomes $2\sqrt{x}-12\sqrt{3x}+15\sqrt{x}$ after simplifying the square root terms.

Step2: Combine like terms

Like terms are terms with the same radical part. Here, $2\sqrt{x}$ and $15\sqrt{x}$ are like terms.
Combining $2\sqrt{x}$ and $15\sqrt{x}$, we get $(2 + 15)\sqrt{x}=17\sqrt{x}$.

So the simplified expression is $17\sqrt{x}-12\sqrt{3x}$.

Answer:

$17\sqrt{x}-12\sqrt{3x}$ (the last option: $17\sqrt{x}-12\sqrt{3x}$)