QuestionFebruary 3, 2026

184. (a) (-4sqrt (5))(5sqrt (10)) (b) (-2sqrt [3](9))(7sqrt [3](9))

184. (a) (-4sqrt (5))(5sqrt (10)) (b) (-2sqrt [3](9))(7sqrt [3](9))
184. (a) (-4sqrt (5))(5sqrt (10)) (b) (-2sqrt [3](9))(7sqrt [3](9))

Solution
4.2(241 votes)

Answer

(a) -100\sqrt{2}, (b) -42 Explanation 1. Simplify the first expression Multiply the coefficients: -4 \times 5 = -20. Multiply the radicals: \sqrt{5} \times \sqrt{10} = \sqrt{50}. Simplify \sqrt{50} to 5\sqrt{2}. 2. Combine the simplified parts Combine: -20 \times 5\sqrt{2} = -100\sqrt{2}. 3. Simplify the second expression Multiply the coefficients: -2 \times 7 = -14. Multiply the cube roots: \sqrt[3]{9} \times \sqrt[3]{9} = \sqrt[3]{81}. 4. Combine the simplified parts Combine: -14 \times \sqrt[3]{81} = -14 \times 3 = -42.

Explanation

1. Simplify the first expression<br /> Multiply the coefficients: $-4 \times 5 = -20$. Multiply the radicals: $\sqrt{5} \times \sqrt{10} = \sqrt{50}$. Simplify $\sqrt{50}$ to $5\sqrt{2}$.<br /><br />2. Combine the simplified parts<br /> Combine: $-20 \times 5\sqrt{2} = -100\sqrt{2}$.<br /><br />3. Simplify the second expression<br /> Multiply the coefficients: $-2 \times 7 = -14$. Multiply the cube roots: $\sqrt[3]{9} \times \sqrt[3]{9} = \sqrt[3]{81}$.<br /><br />4. Combine the simplified parts<br /> Combine: $-14 \times \sqrt[3]{81} = -14 \times 3 = -42$.
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