Question

simplify.

(3\sqrt{8} + 4\sqrt{18} - 5\sqrt{12})

select one:
a. (12\sqrt{2} - 7\sqrt{3})
b. (18\sqrt{2} - 10\sqrt{3})
c. (36)
d. (2\sqrt{14})

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Simplify each radical term

$$ 3\sqrt{8} = 3\sqrt{4 \cdot 2} = 3 \cdot 2\sqrt{2} = 6\sqrt{2} $$

$$ 4\sqrt{18} = 4\sqrt{9 \cdot 2} = 4 \cdot 3\sqrt{2} = 12\sqrt{2} $$

$$ 5\sqrt{12} = 5\sqrt{4 \cdot 3} = 5 \cdot 2\sqrt{3} = 10\sqrt{3} $$

Step 2: Combine like terms

$$ 6\sqrt{2} + 12\sqrt{2} - 10\sqrt{3} = (6 + 12)\sqrt{2} - 10\sqrt{3} = 18\sqrt{2} - 10\sqrt{3} $$

Answer:

b. \(18\sqrt{2} - 10\sqrt{3}\)