Math Problem Statement

Evaluate each of the following: a) cube root of 125, b) negative cube root of 64, c) cube root of -343.

Solution

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a) 1253=5\sqrt[3]{125} = 5

b) 643=4-\sqrt[3]{64} = -4

c) 3433=7\sqrt[3]{-343} = -7

Would you like more clarification on any of these? Or are you ready to move forward with additional questions or explanations?

Here are 5 follow-up questions:

  1. What is 83\sqrt[3]{8}?
  2. How would you find 1003\sqrt[3]{100} without a calculator?
  3. Why does (2)3(-2)^3 result in a negative number?
  4. Can cube roots of fractions be calculated the same way as whole numbers?
  5. What is the cube root of 1, and why?

Tip: When dealing with cube roots of negative numbers, remember that the result will always be negative.

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Math Problem Analysis

Mathematical Concepts

Algebra
Cube Roots
Negative Numbers

Formulas

cube_root(x) = x^(1/3)
-cube_root(x) = -(x^(1/3))

Theorems

For cube roots, the result can be positive or negative depending on the original number. Negative numbers return negative results for cube roots.

Suitable Grade Level

Grades 6-8