Math Problem Statement

Simplify (∛(6x²)) / (∛(5y))

Solution

It looks like you have uploaded an image with a mathematical expression. The expression is:

[ \frac{3\sqrt[3]{6x^2}}{3\sqrt[3]{5y}} ]

We can simplify this expression step by step.

Step 1: Simplify the constants and the cube roots

The constants in the numerator and denominator are both 3, so they will cancel out:

[ \frac{3\sqrt[3]{6x^2}}{3\sqrt[3]{5y}} = \frac{\sqrt[3]{6x^2}}{\sqrt[3]{5y}} ]

Step 2: Simplify the cube roots

We can combine the cube roots into one:

[ \frac{\sqrt[3]{6x^2}}{\sqrt[3]{5y}} = \sqrt[3]{\frac{6x^2}{5y}} ]

Thus, the simplified expression is:

6x25y3\sqrt[3]{\frac{6x^2}{5y}}

Would you like to see more steps or explore related concepts? Feel free to ask!


Here are some related questions that could help deepen your understanding:

  1. How do you simplify expressions with higher roots (like fourth or fifth roots)?
  2. What is the rule for simplifying expressions with variables under a cube root?
  3. How do you handle cube roots when there are coefficients?
  4. What is the difference between cube roots and square roots in terms of simplification?
  5. Can this simplification be applied to other similar expressions involving cube roots?

Tip: When simplifying expressions with roots, always look for common factors in the numerator and denominator that might cancel out to make the expression simpler.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Radicals
Cube Roots
Algebraic Fractions

Formulas

∛(a) / ∛(b) = ∛(a/b)

Theorems

Properties of Radicals

Suitable Grade Level

Grades 8-10