Math Problem Statement

Evaluate the expression \( \sqrt{9} \times \sqrt[3]{9} \).

Solution

The expression in the image you provided appears to be the multiplication of a square root and a cube root:

9×93\sqrt{9} \times \sqrt[3]{9}

To solve this:

  1. First, evaluate the square root of 9: 9=3\sqrt{9} = 3

  2. Next, evaluate the cube root of 9: 932.0801\sqrt[3]{9} \approx 2.0801

  3. Multiply the results: 3×2.08016.24033 \times 2.0801 \approx 6.2403

Thus, the value of the expression is approximately 6.2403.

Would you like more details or have any questions on this? Here are a few follow-up questions to explore further:

  1. How do you simplify the multiplication of roots with different degrees?
  2. What happens when you multiply roots with the same degree?
  3. How do you solve more complex root expressions involving variables?
  4. What are the properties of cube roots and square roots?
  5. How can we estimate irrational roots more accurately?

Tip: When multiplying different roots, it's helpful to express both terms with exponents, as this can make the manipulation easier!

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Math Problem Analysis

Mathematical Concepts

Radicals
Exponents
Multiplication of Roots

Formulas

√a = a^(1/2)
∛a = a^(1/3)
a^m × a^n = a^(m+n)

Theorems

Laws of Exponents
Multiplication Property of Radicals

Suitable Grade Level

Grades 8-10