QuestionAugust 25, 2025

Multiply. sqrt (2)(sqrt (15)-9sqrt (14)) Simplify your answer as much as possible. square square

Multiply. sqrt (2)(sqrt (15)-9sqrt (14)) Simplify your answer as much as possible. square square
Multiply. sqrt (2)(sqrt (15)-9sqrt (14)) Simplify your answer as much as possible. square square

Solution
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Answer

\sqrt{30} - 18\sqrt{7} Explanation 1. Distribute \sqrt{2} Multiply \sqrt{2} with each term inside the parentheses: \sqrt{2} \cdot \sqrt{15} and \sqrt{2} \cdot (-9\sqrt{14}). 2. Simplify each multiplication Use the property \sqrt{a} \cdot \sqrt{b} = \sqrt{ab}. - \sqrt{2} \cdot \sqrt{15} = \sqrt{30} - \sqrt{2} \cdot (-9\sqrt{14}) = -9\sqrt{28} 3. Simplify \sqrt{28} Factor inside the square root: \sqrt{28} = \sqrt{4 \cdot 7} = 2\sqrt{7}. 4. Substitute back Replace \sqrt{28} with 2\sqrt{7} in the expression: -9(2\sqrt{7}) = -18\sqrt{7}. 5. Combine results The expression becomes \sqrt{30} - 18\sqrt{7}.

Explanation

1. Distribute $\sqrt{2}$<br /> Multiply $\sqrt{2}$ with each term inside the parentheses: $\sqrt{2} \cdot \sqrt{15}$ and $\sqrt{2} \cdot (-9\sqrt{14})$.<br /><br />2. Simplify each multiplication<br /> Use the property $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$.<br />- $\sqrt{2} \cdot \sqrt{15} = \sqrt{30}$<br />- $\sqrt{2} \cdot (-9\sqrt{14}) = -9\sqrt{28}$<br /><br />3. Simplify $\sqrt{28}$<br /> Factor inside the square root: $\sqrt{28} = \sqrt{4 \cdot 7} = 2\sqrt{7}$.<br /><br />4. Substitute back<br /> Replace $\sqrt{28}$ with $2\sqrt{7}$ in the expression: $-9(2\sqrt{7}) = -18\sqrt{7}$.<br /><br />5. Combine results<br /> The expression becomes $\sqrt{30} - 18\sqrt{7}$.
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