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:
- How do you calculate the cube root of a number manually?
- What is the cube root of other small numbers like 8 or 27?
- What is the difference between a square root and a cube root?
- How can you find cube roots using a calculator or software?
- 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