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Math Help - Properties of radicals exponents

  1. #1
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    Properties of radicals exponents

    Q1) 48x

    Q2) √ 54x^6


    (all the integers are inside the square root )
    Please answer them in steps
    Thank you,
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Q1) 48x

    Q2) √ 54x^6


    (all the integers are inside the square root )
    Please answer them in steps
    Thank you,
    \sqrt{48 x^2} = \sqrt{16x^2 \cdot 3} = \sqrt{(4x)^2 \cdot 3} ....... I'll leave the rest for you

    \sqrt[3]{54x^6} = \sqrt[3]{27x^6 \cdot 2} = \sqrt[3]{(3x^2)^3 \cdot 2} ....... I'll leave the rest for you
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  3. #3
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    Is this equation correct



    Why can't it be =x^3/1 since there is no value before the square root

    Sorry,but can you please convert your working using fractions?
    Thank you again
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  4. #4
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    Quote Originally Posted by mj.alawami View Post
    Is this equation correct



    Why can't it be =x^3/1 since there is no value before the square root
    1. The equation is true.

    2. \sqrt{\ \ \ } is the short form of \sqrt[2]{\ \ \ }
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  5. #5
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    Quote Originally Posted by earboth View Post
    1. The equation is true.

    2. \sqrt{\ \ \ } is the short form of \sqrt[2]{\ \ \ }
    One final thing can you please convert the equations you sloved using fractions (So it will be easier for me to understand )

    Thank you very much,I really appreciate it
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  6. #6
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    Quote Originally Posted by mj.alawami View Post
    One final thing can you please convert the equations you sloved using fractions (So it will be easier for me to understand )

    Thank you very much,I really appreciate it
    I'm not sure what you mean. There aren't any fractions involved. You only can convert the root sign into a rational exponent:

    <br />
\sqrt{48 x^2} = \sqrt{16x^2 \cdot 3} = \sqrt{(4x)^2 \cdot 3} = \left((4x)^2 \cdot 3 \right)^{\frac12}<br />

    To change a cube root into a rational exponent use \frac13
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