cube root of 375
Understand the Problem
The question is asking for the cube root of the number 375, which means we need to find a number that, when multiplied by itself three times, equals 375.
Answer
7.21
Answer for screen readers
The final answer is approximately 7.21
Steps to Solve
- Understanding cube root notation
The cube root of a number ( x ) is written as ( \sqrt[3]{x} ). We need to find a number ( y ) such that ( y^3 = 375 ).
- Estimate the cube root
Since cube roots can be complex to find, we start by estimating between which two integers the cube root lies. We know that:
$$ 7^3 = 343 \text{ and } 8^3 = 512 $$
Thus, ( \sqrt[3]{375} ) lies between 7 and 8.
- Use a calculator to find a more precise value
To find a more accurate value, we use a calculator to get:
$$ \sqrt[3]{375} \approx 7.21 $$
The final answer is approximately 7.21
More Information
The cube root of a number is the number that, when multiplied by itself twice more (cubed), gives the original number. For 375, this value is approximately 7.21.
Tips
A common mistake when solving for cube roots is not checking where the value lies between two perfect cubes. Always estimate first and then use a calculator for more precision.
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