Math Problem Statement
Simplify the expression 5 / (3√5 + √2)
Solution
The expression shown in the image is:
To simplify this, we will rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, .
Let's go through the steps:
- Multiply the numerator and denominator by :
- Simplify the denominator using the difference of squares formula:
So the denominator becomes:
- Simplify the numerator:
- Final expression:
Thus, the simplified form of the expression is:
Would you like more details or have any questions?
Here are 5 related questions to explore:
- How do you rationalize more complex expressions?
- What are the properties of square roots used in this example?
- Can you generalize the process of rationalizing denominators with square roots?
- What are other ways to simplify fractional expressions with roots?
- How does the difference of squares formula work in algebraic simplifications?
Tip: Rationalizing a denominator helps in making expressions easier to evaluate, especially when dealing with roots.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rationalizing Denominators
Radicals
Formulas
(a√b + c√d)(a√b - c√d) = a²b - c²d
Theorems
Difference of Squares Theorem
Suitable Grade Level
Grades 10-12