Question

perform the indicated operation and simplify.

(6\sqrt{63} + 6\sqrt{28})

(6\sqrt{63} + 6\sqrt{28} = \square)
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Simplify each radical term

Find the largest perfect square factors for the radicands \(63\) and \(28\):

$$ 63 = 9 \times 7 $$

$$ 28 = 4 \times 7 $$

Substitute these back into the expression:

$$ 6\sqrt{63} + 6\sqrt{28} = 6\sqrt{9 \times 7} + 6\sqrt{4 \times 7} $$

Simplify by taking the square roots of the perfect squares:

$$ 6 \times 3\sqrt{7} + 6 \times 2\sqrt{7} $$

$$ 18\sqrt{7} + 12\sqrt{7} $$

Step 2: Combine like terms

Add the coefficients of the like radical terms:

$$ (18 + 12)\sqrt{7} = 30\sqrt{7} $$

Answer:

\(30\sqrt{7}\)