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)

2. Originally Posted by dempc
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 $\displaystyle \textrm{dom}: x \geq -2, \textrm{ran}: y \geq 0$.