State, giving reason, wether the given number is rational or irrational: (i) (3 + √5) (ii) (-1 + √3) (iii) 5√6 (iv) -√7 (v) √6/4 (vi) 3/√2 (vii) (3 + √3) (3 - √3)

Question

KnowledgeBoat · Accepted Answer

(i) Given, 3 is a rational number as it can be expressed in the form of , where p and q are integers and q 0. is an irrational number as it is a square root of a non-perfect square i.e. 5. The sum of a rational number and an irrational number is always irrational. Hence, is a irrational number. (ii) Given, -1 is a rational number as it can be expressed in the form of , where p and q are integers and q 0. is an irrational number as it is a square root of a non-perfect square i.e. 3. The sum of a rational number and an irrational number is always irrational. Hence, is a irrational number. (iii) Given, 5 is a rational number as it can be expressed in the form of , where p and q are integers and q 0. is an irrational number as it is a square root of a non-perfect square i.e. 6. The product of a rational number and an irrational number is always irrational. Hence, is an irrational number. (iv) Given, , is an irrational number as it is a square root of a non-perfect square i.e. 7. ∴ is an irrational number. Hence, is an irrational number. (v) Given, 4 is a rational number as it can be expressed in the form of , where p and q are integers and q 0. is an irrational number as it is a square root of a non-perfect square i.e. 6. The division of a rational number and an irrational number is always irrational. Hence, is an irrational number. (vi) Given, 3 is a rational number as it can be expressed in the form of , where p and q are integers and q 0. is an irrational number as it is a square root of a non-perfect square i.e. 2. The division of a rational number and an irrational number is always irrational. Hence, is an irrational number. (vii) Given, 3 is a rational number as it can be expressed in the form of , where p and q are integers and q 0. Hence, is a rational number.

Mathematics

State, giving reason, wether the given number is rational or irrational: (i) (3 + √5) (ii) (-1 + √3) (iii) 5√6 (iv) -√7 (v) √6/4 (vi) 3/√2 (vii) (3 + √3) (3 - √3)

Rational Irrational Nos

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