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Step-by-step explanation:
multiplying it by its conjugate
5√2+3√5. 5√2+3√5
--------------- * ----------------
5√2-3√5. 5√2+3√5
= (5√2+3√5)²
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(5√2)²-(3√5)²
= 25*2+9*5+15*√10
------------------------------
25*2-9*5
= 50+45+15√10
------------------------
50-45
= 95 + 15√10
---------------------
5
= 19+3√10
therefore a = 19 and b = 3
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