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Simplify each of the following by ration...

Simplify each of the following by rationalizing the denominator: I(I)`(7+3sqrt(5))/(7-3sqrt(5))` (ii) `(2\ sqrt(3)-\ sqrt(5))/(2sqrt(2)+\ 3sqrt(3))`

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Let's simplify the given expressions by rationalizing the denominators step by step. ### Part (i): Simplify \(\frac{7 + 3\sqrt{5}}{7 - 3\sqrt{5}}\) **Step 1: Multiply by the Conjugate** To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator, which is \(7 + 3\sqrt{5}\). \[ ...
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(2sqrt(7))/(sqrt(5)-sqrt(3))

Simplify each of the following by rationalising the denominator,(1)/(5+sqrt(2)) (ii) (5+sqrt(6))/(5-sqrt(6)) (iii) (7+3sqrt(5))/(7-3sqrt(5)) (iv) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))

Knowledge Check

  • (5sqrt(7)+2sqrt(7))(6sqrt(7)+3sqrt(7))=?

    A
    401
    B
    415
    C
    417
    D
    441

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