show that the sum and product of two rational numbers (5+root 3) and (5-root3) are rational numbers
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the sum of (5 + root 3) and (5 - root 3)
= 5 + root 3 + 5 - root 3
= 10 ( since +root 3 and -root 3 get cancelled due to opposite sign)
The product of (5 + root 3) and (5 - root 3)
= (5 + root 3) (5 - root 3) = 5^2 - (root 3)^2
= 25 - 3
= 22
Note: (using identity formula )
(a+b)(a-b) = a^2 - b^2
= 5 + root 3 + 5 - root 3
= 10 ( since +root 3 and -root 3 get cancelled due to opposite sign)
The product of (5 + root 3) and (5 - root 3)
= (5 + root 3) (5 - root 3) = 5^2 - (root 3)^2
= 25 - 3
= 22
Note: (using identity formula )
(a+b)(a-b) = a^2 - b^2
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