Math Problem Statement

Which integer is closest to the cube root of 7?

Solution

The question asks: "Which integer is closest to the cube root of 7 (³√7)?"

Let's break this down.

The cube root of 7 is the number that, when multiplied by itself three times, equals 7. To find this, we can approximate:

  • 2³ = 8 (which is slightly larger than 7).
  • 1³ = 1 (which is much smaller than 7).

Thus, ³√7 must lie between 1 and 2. Let's calculate a more accurate value:

The cube root of 7 is approximately 1.913.

The closest integer to 1.913 is 2.

Would you like more details, or have any questions?

Here are 5 related questions:

  1. How do you calculate the cube root of a number manually?
  2. What is the cube root of other small numbers like 8 or 27?
  3. What is the difference between a square root and a cube root?
  4. How can you find cube roots using a calculator or software?
  5. How does the concept of roots apply in geometry?

Tip: Cube roots can be estimated by knowing powers of numbers, which helps you quickly narrow down the closest integer.

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Math Problem Analysis

Mathematical Concepts

Cube Root
Approximations

Formulas

x = ³√y, where x^3 = y

Theorems

Properties of Cube Roots

Suitable Grade Level

Grades 6-8