Question

algebra: concepts and connections - plc radical equations which equation is a radical equation? options: $xsqrt{3} + x = sqrt3{2x}$, $4p = sqrt{-3} + p$, $5 - sqrt3{8} = ysqrt{16}$, $7sqrt{11} - w = -34$

Explanation:

A radical equation is defined as an equation where a variable is contained within a radical (square root, cube root, etc.). Let's analyze each option:

1. $x\sqrt{3} + x = \sqrt[3]{2x}$: The variable $x$ is inside the cube root $\sqrt[3]{2x}$, so this fits the definition of a radical equation.
2. $4p = \sqrt{-3} + p$: $\sqrt{-3}$ is a constant imaginary number, no variable is inside the radical.
3. $5 - \sqrt[3]{8} = y\sqrt{16}$: $\sqrt[3]{8}=2$ and $\sqrt{16}=4$ are both constants, no variable is inside a radical.
4. $7\sqrt{11} - w = -34$: $\sqrt{11}$ is a constant, no variable is inside a radical.

Answer:

$x\sqrt{3} + x = \sqrt[3]{2x}$