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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) : 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 = + 3 − 2r √3, which implies √3 = .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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