If √ 15 = 3.8729 then what is (√5 + √3)/(√5 - √3)?

2024

If √ 15 = 3.8729 then what is (√5 + √3)/(√5 - √3)?

  1. A.

    7.8729

  2. B.

    6.8729

  3. C.

    5.8729

  4. D.

    4.8729

Attempted by 3 students.

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Correct answer: A

Step-by-Step Solution

To solve the expression (sqrt(5) + sqrt(3)) / (sqrt(5) - sqrt(3)) given that sqrt(15) = 3.8729, we follow these steps:

  1. Rationalize the denominator: Multiply both the numerator and the denominator by the conjugate of the denominator, which is (sqrt(5) + sqrt(3)). Expression = [(sqrt(5) + sqrt(3)) / (sqrt(5) - sqrt(3))] * [(sqrt(5) + sqrt(3)) / (sqrt(5) + sqrt(3))]

  2. Simplify the expression:

    • Numerator: (sqrt(5) + sqrt(3))^2 = (sqrt(5))^2 + (sqrt(3))^2 + 2 * sqrt(5) * sqrt(3) = 5 + 3 + 2 * sqrt(15) = 8 + 2 * sqrt(15)

    • Denominator: (sqrt(5) - sqrt(3)) * (sqrt(5) + sqrt(3)) = (sqrt(5))^2 - (sqrt(3))^2 = 5 - 3 = 2

  3. Complete the calculation: Expression = (8 + 2 * sqrt(15)) / 2 Expression = (8 / 2) + (2 * sqrt(15) / 2) Expression = 4 + sqrt(15)

  4. Substitute the given value:

    • Given sqrt(15) = 3.8729

    • Final Result = 4 + 3.8729 = 7.8729

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