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Can you help me solve this math problem dealing with radicals?
√6 + √5 over 2 multiply by √6 - √5 over 2 (like a fraction when it says "over 2")
Simplify and show work.
2 Answers
- 1 decade agoFavorite Answer
(√6 + √5)(√6-√5)/4 = (√6 √6 + √6√5 - √6√5 -√5√5)/4 = 6-5/4 = 1/4
- MathBioMajorLv 71 decade ago
The product of the conjugates (√6 + √5) and (√6 - √5) is the difference of two squares, and is in the form (a + b) ∙ (a - b) = (a² - b²). So let a = √6 and b = √5. Then we obtain this when we multiply the two fractions together:
(√6 + √5)/2 ∙ (√6 - √5)/2 = [(√6)² - (√5)²]/(2)² = (6 - 5)/4 = 1/4.
