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Thread: Another Radical Question

  1. #1
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    Another Radical Question

    1. The square root of 2 times (x+the sq root of 8)

    the sq root of 2 is outside the parenthesis

    My answer = x sq root of 2 + 4

    2. Rewrite using a radical then simplify: 8 to the power of 3\5

    3. Find the domain and rage of the function f (x) = Sq root of (3x+6)
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  2. #2
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    Quote Originally Posted by dempc View Post
    1. The square root of 2 times (x+the sq root of 8)

    the sq root of 2 is outside the parenthesis

    My answer = x sq root of 2 + 4

    2. Rewrite using a radical then simplify: 8 to the power of 3\5

    3. Find the domain and rage of the function f (x) = Sq root of (3x+6)
    1.
    $\displaystyle \sqrt{2}(x + \sqrt{8}) = \sqrt{2}x + \sqrt{2}\sqrt{8}$

    $\displaystyle = \sqrt{2}x + 2\sqrt{2}\sqrt{2}$

    $\displaystyle = \sqrt{2}x + 4$


    2. $\displaystyle 8^{\frac{3}{5}} = \sqrt[5]{8^3}$

    $\displaystyle = \sqrt[5]{512}$


    3. You can only have the square root of a nonnegative number.

    So $\displaystyle 3x + 6 \geq 0 \implies x \geq -2$


    At $\displaystyle x = -2, y = \sqrt{0} = 0$, and y is increasing.


    So $\displaystyle \textrm{dom}: x \geq -2, \textrm{ran}: y \geq 0$.
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