What is the cube root of 2?
Understand the Problem
The question is asking for the cube root of the number 2. To solve this, we need to determine the value that, when multiplied by itself three times, equals 2.
Answer
The cube root of 2 is approximately $\sqrt[3]{2} \approx 1.25992$.
Answer for screen readers
The cube root of 2 is approximately $\sqrt[3]{2} \approx 1.25992$.
Steps to Solve
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Understanding Cube Root
The cube root of a number $x$ is the value $y$ such that $y^3 = x$. In this case, we want to find $y$ such that $y^3 = 2$. -
Expressing Mathematically
We express the cube root of 2 mathematically as:
$$ y = \sqrt[3]{2} $$ -
Using a Calculator or Approximation
To find the numerical value of $y$, we can either use a scientific calculator or estimate the value by trial and error.
For instance, try approximate values:
- If $1.2^3 = 1.728$
- If $1.3^3 = 2.197$
This suggests that the cube root of 2 is between 1.2 and 1.3.
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Refining the Approximation
Narrow it down:
- If $1.25^3 = 1.953125$ (too low)
- If $1.26^3 = 2.000376$ (too high)
This indicates that the cube root of 2 is approximately 1.25.
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Final Value
To get a more precise result, using a calculator gives us:
$$ \sqrt[3]{2} \approx 1.25992 $$
The cube root of 2 is approximately $\sqrt[3]{2} \approx 1.25992$.
More Information
The cube root of a number is important in various fields, such as geometry, physics, and engineering, as it helps in calculating volumes and dimensions. The cube root of 2 is also related to the dimensions of a cube with a volume of 2 cubic units.
Tips
- Misunderstanding cube roots: Some may confuse cube roots with square roots. Remember that cube roots are what you multiply three times (not twice).
- Rounding too early: When estimating or calculating, rounding before reaching the final answer can lead to inaccuracies.
