Higher Roots Worksheet with Answer Key

What's on the worksheet

1. Find each root, or say why it is not a real number:
   \sqrt[5]{-1024}\sqrt[4]{-16}-\sqrt[5]{-32}\sqrt[9]{-512}\sqrt[4]{\frac{81}{625}}
2. Solve each equation over the real numbers; some have two, one or no solutions.
   x^7 = -1285x^4 - 3 = 77\dfrac{x^6}{2} + 9 = 1(x + 1)^6 = 64-2(x - 4)^5 = 64
3. Simplify each expression, using absolute value only where needed.
   \sqrt[4]{81x^4}\sqrt[5]{32x^{10}y^5}\sqrt[4]{x^4y^8}\sqrt[4]{16x^{20}}\sqrt[4]{(x - 3)^4}
4. Simplify each product or quotient of roots to a whole number or a smallest root.
   \sqrt[4]{27} \cdot \sqrt[4]{3}\dfrac{\sqrt[5]{-486}}{\sqrt[5]{2}}\sqrt[4]{162}\sqrt[5]{-96}\sqrt[4]{6} \cdot \sqrt[4]{24}
5. Word problem: a poster line shrunk by the same factor on each copy.
6. Check Daniel's claim about a sum of roots at a negative input and write it correctly.