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CBSE Class 10 Standard Math 2026 All Sets Solved Paper

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Question : 19 of 20
Marks: +1, -0
Assertion (A) : (3+5)(\sqrt{3} + \sqrt{5}) is an irrational number.
Reason (R) : Sum of the any two irrational numbers is always irrational.
Solution:  
Assertion (A): √3 + √5 is indeed irrational.
If it were rational, say r, then √5 = r − √3.
Squaring both sides gives 5 =r2r^{2} + 3 − 2r √3, which implies √3 = r2−22r\frac{r^{2} - 2}{2r}.
Since the RHS is rational and √3 is irrational, this is a contradiction.
Thus, (A) is true.
Reason (R): This statement is false.
Counter-example: Consider two irrational numbers √2 and − √2.
Sum: √2 + (−√2) = 0, which is a rational number.
Since the Reason is false, the option is (C)
Assertion (A) is true, but Reason (R) is false
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