Questions: Add or subtract, as indicated. 6 sqrt(5 x) - 4 sqrt(5 x) + 15 sqrt(5 x) 6 sqrt(5 x) - 4 sqrt(5 x) + 15 sqrt(5 x) = (Simplify your answer. Type an exact answer, using radicals as needed.)

Add or subtract, as indicated.
6 sqrt(5 x) - 4 sqrt(5 x) + 15 sqrt(5 x)
6 sqrt(5 x) - 4 sqrt(5 x) + 15 sqrt(5 x) =
(Simplify your answer. Type an exact answer, using radicals as needed.)

Transcript text: Add or subtract, as indicated. \[ \begin{array}{l} 6 \sqrt{5 x}-4 \sqrt{5 x}+15 \sqrt{5 x} \\ 6 \sqrt{5 x}-4 \sqrt{5 x}+15 \sqrt{5 x}= \end{array} \] $\square$ (Simplify your answer. Type an exact answer, using radicals as needed.)

Solution

Solution Steps

To simplify the expression, we need to combine like terms. The terms $6 \sqrt{5x}$, $-4 \sqrt{5x}$, and $15 \sqrt{5x}$ all have the same radical part, $\sqrt{5x}$. Therefore, we can add or subtract their coefficients directly.

Step 1: Identify Like Terms

We start with the expression $6 \sqrt{5x} - 4 \sqrt{5x} + 15 \sqrt{5x}$. All terms contain the common factor $\sqrt{5x}$.

Step 2: Combine Coefficients

Next, we combine the coefficients of the like terms: \[ 6 + (-4) + 15 = 17 \]

Step 3: Write the Simplified Expression

The simplified expression can now be written as: \[ 17 \sqrt{5x} \]