show that (2+√5)(2-√5)(3+√2)(3-√2) is a rational number

Question

show that (2+√5)(2-√5)(3+√2)(3-√2) is a rational number

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Mary 1 day 2021-10-13T03:23:51+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-13T03:25:14+00:00

    Answer:

    (2 + √5)(2-√5)(3+√2)(3-√2)

    = (2² – √5²)(3² – √2²)

    = ( 4 – 5)( 3 -2)

    = -1 × 1

    = -1

    that is rational number.

    Step-by-step explanation:

    formula used

    ( a+ b)(a – b) = a² – b²

    0
    2021-10-13T03:25:26+00:00

     \implies(2 +  \sqrt{5})(2 -  \sqrt{5})(3 +  \sqrt{2})(3 -  \sqrt{2}) \\  \\  \\ \implies( {2}^{2}   -   { \sqrt{5} }^{2})( {3}^{2}  -  { \sqrt{2} }^{2}) \\  \\  \\  \implies(4 - 5)(9 - 2) \\  \\  \\  \implies - 1 \times 7 \\  \\  \\ \implies - 7

    so -7 is a rational number

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