Math Problem Statement
Identify the cube root of 5 (³√5).
Solution
The expression in the image is , which represents the cube root of 5. To express this in another form, we can write it as:
Understanding the Concept:
- A cube root of a number is the value that, when multiplied by itself three times, gives .
- In this case, is the number that, when multiplied by itself three times, equals 5.
Approximate Value:
Using a calculator, the cube root of 5 is approximately:
Let me know if you'd like further details or clarifications!
Here are five related questions to deepen your understanding:
- How do we calculate higher roots, such as the fourth root or fifth root?
- What is the difference between square roots and cube roots in terms of how they are solved?
- Can be simplified further without using a calculator?
- How is the cube root of a negative number calculated?
- How do cube roots relate to exponents in algebraic expressions?
Tip: Cube roots can also be solved using exponentiation rules. For example, is the same as .
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Math Problem Analysis
Mathematical Concepts
Cube Roots
Radical Expressions
Exponentiation
Formulas
³√x = x^(1/3)
x^n = a (where a is the result of multiplying x by itself n times)
Theorems
Radical Exponent Rule: a^(1/n) is the nth root of a.
Exponentiation: x^(m/n) = (n√x)^m
Suitable Grade Level
Grades 8-10