Question

add or subtract as indicated. assume all variables are greater than or equal to zero.

(6\sqrt{3x} - 3\sqrt{3x} + 9\sqrt{3x})

(6\sqrt{3x} - 3\sqrt{3x} + 9\sqrt{3x} = \\) (type an exact answer, using radicals as needed.)

Explanation:

⚡ Using what you learned: Roots and Radicals

Step 1: Identify like radicals

The given expression is:

$$ 6\sqrt{3x} - 3\sqrt{3x} + 9\sqrt{3x} $$

All three terms share the exact same radical part, \(\sqrt{3x}\). This means they are "like terms" and can be combined by adding or subtracting their coefficients.

Step 2: Combine the coefficients

Group the coefficients together:

$$ (6 - 3 + 9)\sqrt{3x} $$

Calculate the sum:

$$ 6 - 3 = 3 $$

$$ 3 + 9 = 12 $$

Combine to get the final simplified term:

$$ 12\sqrt{3x} $$

Answer:

$$ 12\sqrt{3x} $$