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3 September, 05:51

Rationalize the denominator and simplify 6/√2-√3

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  1. 3 September, 06:06
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    =3 √6 - 3 √5

    Explanation:

    3 √5 + √6

    We rationalise the denominator by multiplying the expression by the conjugate of the denominator. √5 - √6

    3⋅ (√5 - √6) (√5 + √6) ⋅ (√5 - √6)

    = 3⋅ (√5) + 3⋅ ( - √6) (√5 + √6) ⋅ (√5 - √6)

    = 3 √5 - 3 √6 (√5 + √6) ⋅ (√5 - √6)

    Applying identity

    (a+b) (a-b) = a2 - b2 to the denominator.

    = 3 √5 - 3 √6 (√5) 2 - (√6) 2

    = 3 √5 - 3 √6 5-6

    = 3 √5 - 3 √6 - 1

    =-3 √5 + 3 √6

    =3 √6 - 3 √ 5
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