Math Problem Statement
rationalise the denominator
Solution
The given expression is:
To rationalize the denominator, we need to eliminate the cube root from the denominator. Here's how we can do it:
Steps to rationalize the denominator:
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The denominator is . We want to multiply both the numerator and the denominator by the cube root of a number that will make the denominator a whole number. We need to find a factor that will make a perfect cube.
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Since , we multiply both the numerator and denominator by , which is the cube root of 3.
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Now multiply:
[ \frac{3}{\sqrt[3]{24}} \times \frac{\sqrt[3]{3}}{\sqrt[3]{3}} = \frac{3 \times \sqrt[3]{3}}{\sqrt[3]{24} \times \sqrt[3]{3}} ]
- The denominator becomes:
[ \sqrt[3]{24 \times 3} = \sqrt[3]{72} ]
- So, the expression becomes:
[ \frac{3 \times \sqrt[3]{3}}{\sqrt[3]{72}} ]
This is the rationalized form of the original expression.
Would you like further details or have any other questions?
Related questions:
- How can we simplify cube roots in expressions?
- What is the general method for rationalizing higher-order roots like square or cube roots?
- How do you evaluate cube roots of numbers such as 24 or 72?
- Can you apply the same rationalization process to square roots or other radical expressions?
- What is the significance of rationalizing denominators in mathematics?
Tip: When rationalizing cube roots or higher roots, always multiply by the factor that will make the base inside the root a perfect cube (or square for square roots).
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Math Problem Analysis
Mathematical Concepts
Rationalizing Denominators
Cube Roots
Formulas
Rationalizing a denominator using cube roots
Theorems
Cube root multiplication to rationalize denominators
Suitable Grade Level
Grades 9-11