Printable worksheets focused on solving equations of the form $x^2 = k$ and $x^3 = k$ provide practice in isolating the variable 'x'. For $x^2 = k$, the solution involves taking the square root of both sides, remembering that there are often two solutions: a positive and a negative root. For $x^3 = k$, the solution requires taking the cube root, which results in only one real solution. These worksheets aim to reinforce understanding through vocabulary, application, and critical thinking exercises.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Square Root | A. A value that, when multiplied by itself, equals a given number. |
| 2. Cube Root | B. A value that, when multiplied by itself three times, equals a given number. |
| 3. Variable | C. A symbol (usually a letter) representing an unknown value in an equation. |
| 4. Equation | D. A mathematical statement that two expressions are equal. |
| 5. Solution | E. The value(s) that satisfy an equation. |
Complete the following paragraph with the correct words:
To solve the equation $x^2 = k$, we need to find the ______ ______ of $k$. Remember that a positive number has both a ______ and a ______ square root. To solve the equation $x^3 = k$, we find the ______ ______ of $k$. Unlike square roots, cube roots have only ______ real solution for any real number $k$.
Explain why the equation $x^2 = -4$ has no real solutions, but the equation $x^3 = -8$ does have a real solution.
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