Math Problem Statement

Identify the cube root of 5 (³√5).

Solution

The expression in the image is 53\sqrt[3]{5}, which represents the cube root of 5. To express this in another form, we can write it as:

5135^{\frac{1}{3}}

Understanding the Concept:

  • A cube root of a number xx is the value that, when multiplied by itself three times, gives xx.
  • In this case, 53\sqrt[3]{5} is the number that, when multiplied by itself three times, equals 5.

Approximate Value:

Using a calculator, the cube root of 5 is approximately:

531.710\sqrt[3]{5} \approx 1.710

Let me know if you'd like further details or clarifications!

Here are five related questions to deepen your understanding:

  1. How do we calculate higher roots, such as the fourth root or fifth root?
  2. What is the difference between square roots and cube roots in terms of how they are solved?
  3. Can 51/35^{1/3} be simplified further without using a calculator?
  4. How is the cube root of a negative number calculated?
  5. How do cube roots relate to exponents in algebraic expressions?

Tip: Cube roots can also be solved using exponentiation rules. For example, x3\sqrt[3]{x} is the same as x1/3x^{1/3}.

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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