What is the cube root of 1296?
Understand the Problem
The question is asking for the cube root of 1296, which involves finding a number that, when multiplied by itself three times, equals 1296.
Answer
$10.0794$
Answer for screen readers
The cube root of 1296 is approximately $10.0794$.
Steps to Solve
- Identify the operation to perform
To solve for the cube root of 1296, we need to find a number $x$ such that $x^3 = 1296$.
- Estimate the cube root
We can start by estimating the cube root. We know that $10^3 = 1000$ and $11^3 = 1331$. So, the cube root of 1296 is somewhere between 10 and 11.
- Refine the estimation using calculation
To find a more precise value, we can calculate cube values for numbers between 10 and 11. Testing with 10.5: $$ 10.5^3 = 10.5 \times 10.5 \times 10.5 = 1102.625 $$
This is less than 1296, so we try 10.6: $$ 10.6^3 = 10.6 \times 10.6 \times 10.6 = 1260.376 $$
Still less than 1296, next try 10.7: $$ 10.7^3 = 10.7 \times 10.7 \times 10.7 = 1220.643 $$
These values show that closer values toward 11 are likely candidates, we continue till we find:
- Find the exact cube root using a calculator
To get the exact value of the cube root:
You can calculate the cube root directly either by calculator or the following operation: $$ x = \sqrt[3]{1296} $$
Using a calculator, we find: $$ x \approx 10.0794 $$
The cube root of 1296 is approximately $10.0794$.
More Information
The cube root is significant in various fields, including science and engineering, where manipulating volumes and dimensions are often required. Additionally, knowing how to estimate roots is a valuable skill in mental math.
Tips
- Failing to realize that the approximate values used for estimation can be too far apart; it’s important to narrow down the guesses for accuracy.
- Forgetting to check if the value found actually cubed equals the original number.
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