Math Problem Statement
3√2 / 4+2√5
Solution
The expression you provided is:
To simplify this, we rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of is .
- Multiply both the numerator and the denominator by :
- First, simplify the denominator using the difference of squares formula :
- Now, simplify the numerator:
- Putting it all together, we now have:
So, the simplified expression is:
Would you like further details or have any questions?
Here are five related questions you might find interesting:
- How do you rationalize other complex denominators?
- What is the difference between a rational and an irrational number?
- Can you apply the difference of squares to any radical expression?
- What is the general form of a conjugate and how is it useful in simplifications?
- How would this simplification change if there were additional radicals in the numerator?
Tip: Always multiply by the conjugate to eliminate square roots from the denominator when rationalizing!
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Math Problem Analysis
Mathematical Concepts
Algebra
Radical Expressions
Rationalization
Difference of Squares
Formulas
Difference of squares: (a + b)(a - b) = a^2 - b^2
Rationalizing denominators using conjugates
Theorems
Difference of Squares Theorem
Suitable Grade Level
Grades 10-12