What is the simplified form of 3 startroot 135 endroot?

What is the simplified form of 3 startroot 135 endroot?

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  1. [tex]\bf 3\sqrt{135}~~ \begin{cases} 135=&3\cdot 3\cdot 15\\ &3^2\cdot 15 \end{cases}\implies 3\sqrt{3^2\cdot 15}\implies 9\sqrt{15}[/tex]

  2. [tex]9 \sqrt{135}[/tex]

    Step-by-step explanation:

    Express 135 as a product of 15 and 9:

    [tex]135=15*9[/tex]

    So:

    [tex]3\sqrt{15*9}[/tex]

    Now, use the following property:

    [tex]\sqrt[n]{a*b} =\sqrt[n]{a}\hspace{3} \sqrt[n]{b}[/tex]

    Therefore:

    [tex]3\sqrt{15} \sqrt{9}[/tex]

    Since the square root of 9 is 3, the simplified form of [tex]3\sqrt{135}[/tex]:

    [tex]3\sqrt{15} \sqrt{9}=3*3\sqrt{15} =9\sqrt{15}[/tex]

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