The process of solving radical equations requires us to first isolate the radical on a single side of the equation, and then proceed to square both sides with the aim to remove the radical. If the equation includes multiple radicals, this process might need to be repeated. It is crucial to verify the solutions, as the act of squaring can potentially introduce irrelevant solutions.
| Topic | Problem | Solution |
|---|---|---|
| None | Question 1 of 33 Solve $\sqrt{4 x+24}=x+3$. Check… | Square both sides of the equation to get rid of the square root, resulting in \(4x + 24 = (x + 3)^2… |
| None | Find all possible solutions. Give your answers in… | Given the equation \(\sqrt{-4x+4}+5=8x\) |
| None | Solve the following equation and check for extran… | The given equation is \(\sqrt[4]{-2 x^{2}+1}=-x\). |
| None | Solve the following equation and check for extran… | The given equation is \(\sqrt[4]{6 x^{2}-8}=-x\). |
| None | Solve the following equation. Round your answer(s… | The given equation is a radical equation, which means it contains square roots. To solve this type … |
| None | Solve the following equation. \[ -27 x^{-3 / 4}=-… | The given equation is \(-27 x^{-3 / 4}=-64\). |
| None | $2 \sqrt{x}-14=\frac{288}{\sqrt{x}}$ | Given the equation \(2 \sqrt{x}-14=\frac{288}{\sqrt{x}}\) |
| None | Solve the equation. \[ (x-3)^{2 / 5}=4 \] | Given the equation \((x-3)^{2 / 5}=4\) |
| None | Solve the equation. \[ x-\sqrt{12-4 x}=0 \] | First, we note that $x$ must be less than or equal to $3$, since $\sqrt{12-4x}$ is undefined if $x>… |
| None | $\sqrt{x+11} \sqrt{x-4}=3$ | Square both sides of the equation: \((\sqrt{x+11} \sqrt{x-4})^2 = 3^2\) |
| None | b) $\sqrt{x-1 \sqrt{2 x-2}}=2$ | \(\sqrt{x-1 \sqrt{2 x-2}}=2\) |