State whether the given statement is true or false.
(i) the sum of two rationals is always rational.
(ii) the product of two rational is always rational.
(iii) The sum of two irrational is always an irrational.
(iv) the product of two irrational is always an irrational.
(v) the sum of a rational and an irrational is irrational.
(vi) The product of a rational and an irrational is irrational.

Question

Filo · Accepted Answer

(i) True(ii) True(iii) False Reason :Sum of two irrational can be rational let us take an example,Consider two irrational numbers :  (3+√2)and(3−√2)Sum :  (3+√2)+(3−√2)=3+√2+3−√2=6which is rational(iv) falseReason :Product of two irrational numbers can be rational. let us take an example, consider two rational numbers : (3+√2)and(3−√2)Product : (3+√2)(3−√2)=(3)2−(√2)2=9−2=7; which is rational(v) True(vi) True

Question Text	State whether the given statement is true or false. (i) the sum of two rationals is always rational. (ii) the product of two rational is always rational. (iii) The sum of two irrational is always an irrational. (iv) the product of two irrational is always an irrational. (v) the sum of a rational and an irrational is irrational. (vi) The product of a rational and an irrational is irrational.
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