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QQ MULTIPLE CHOICE Question 2 Simplify: 8sqrt (3)cdot 9sqrt (27) A 24sqrt (3) B 72sqrt (27) C 648 D 1,944

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QQ MULTIPLE CHOICE
Question 2
Simplify: 8sqrt (3)cdot 9sqrt (27)
A 24sqrt (3)
B 72sqrt (27)
C 648
D 1,944

QQ MULTIPLE CHOICE Question 2 Simplify: 8sqrt (3)cdot 9sqrt (27) A 24sqrt (3) B 72sqrt (27) C 648 D 1,944

Solução

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BentoVeterano · Tutor por 10 anos

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To simplify the expression \(8\sqrt{3} \cdot 9\sqrt{27}\), we can follow these steps:<br /><br />1. Simplify \(\sqrt{27}\):<br /> \[<br /> \sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3}<br /> \]<br /><br />2. Substitute \(\sqrt{27}\) with \(3\sqrt{3}\) in the original expression:<br /> \[<br /> 8\sqrt{3} \cdot 9\sqrt{27} = 8\sqrt{3} \cdot 9 \cdot 3\sqrt{3}<br /> \]<br /><br />3. Combine the constants and the radicals:<br /> \[<br /> 8 \cdot 9 \cdot 3 \cdot \sqrt{3} \cdot \sqrt{3} = 8 \cdot 9 \cdot 3 \cdot 3 = 648<br /> \]<br /><br />Therefore, the simplified form of the expression is:<br />\[<br />648<br />\]<br /><br />So, the correct answer is:<br />C) 648
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