Pergunta

simplest radical form. 2sqrt (9x^6y^3) Answer Attempt 1 out of 3 square
Solução

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LeonardoVeterano · Tutor por 9 anos
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To simplify the expression \(2\sqrt{9x^6y^3}\), we need to break it down into simpler components.<br /><br />First, let's simplify the square root part:<br />\[ \sqrt{9x^6y^3} \]<br /><br />We know that:<br />\[ \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \]<br /><br />So, we can separate the terms under the square root:<br />\[ \sqrt{9x^6y^3} = \sqrt{9} \cdot \sqrt{x^6} \cdot \sqrt{y^3} \]<br /><br />Now, let's simplify each square root individually:<br />\[ \sqrt{9} = 3 \]<br />\[ \sqrt{x^6} = x^3 \]<br />\[ \sqrt{y^3} = \sqrt{y^2 \cdot y} = \sqrt{y^2} \cdot \sqrt{y} = y \cdot \sqrt{y} \]<br /><br />Putting it all together:<br />\[ \sqrt{9x^6y^3} = 3 \cdot x^3 \cdot y \cdot \sqrt{y} = 3x^3y\sqrt{y} \]<br /><br />Now, we multiply this result by the 2 outside the square root:<br />\[ 2\sqrt{9x^6y^3} = 2 \cdot 3x^3y\sqrt{y} = 6x^3y\sqrt{y} \]<br /><br />So, the simplified form of \(2\sqrt{9x^6y^3}\) is:<br />\[ \boxed{6x^3y\sqrt{y}} \]
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