Math Problem Statement

Find the real-number root using a calculator. Round your answer to the nearest thousandth. \( \sqrt[3]{942} \)

Solution

To solve 9423\sqrt[3]{942} and round to the nearest thousandth, we can use a calculator. The cube root of 942 is computed as follows:

94239.810\sqrt[3]{942} \approx 9.810

So, the real-number root of 9423\sqrt[3]{942}, rounded to the nearest thousandth, is 9.810.

Would you like further explanation or help with another problem? Here are some related questions for practice:

  1. What is the cube root of 729?
  2. How can you estimate cube roots without a calculator?
  3. What is the difference between cube roots and square roots?
  4. How would you solve 1253\sqrt[3]{125} by hand?
  5. What are the applications of cube roots in real-life scenarios?

Tip: When rounding to the nearest thousandth, ensure you look at the fourth decimal place to decide whether to round up or stay the same.

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Math Problem Analysis

Mathematical Concepts

Cube roots
Rational numbers
Rounding to the nearest thousandth

Formulas

\( \sqrt[3]{x} \): Cube root of a number

Theorems

Properties of radicals

Suitable Grade Level

Grades 8-10