Classify the rational and irrational numbers from the following : (i) 5 (ii) 9/14 (iii) √3 (iv) π (v) 3.1416 (vi) √4 (vii) -√5 (viii) ∛8 (ix) ∛3 (x) 2√6 (xi) 0.36 (xii) 0.202202220... (xiii) 2/√3 (xiv) 22/7

Question

KnowledgeBoat · Accepted Answer

(i) 5 can be expressed in the form , where p and q are integers and q 0. Hence, 5 is a rational number. (ii) can be expressed in the form , where p and q are integers and q 0. Hence, is a rational number. (iii) is square root of non-perfect square i.e. 3. Hence, is an irrational number. (iv) π is a non-terminating and non-repeating decimal. Hence, π is a irrational number. (v) 3.1416 is a terminating decimal, so it can be expressed in the form of , where p and q are integers and q 0. Hence, 3.1416 is a rational number. (vi) is square root of perfect square i.e. 4. . Hence, is a rational number. (vii) is square root of non-perfect square. Hence, is an irrational number. (viii) Given, . ∴ can be expressed in the form of , where p and q are integers and q 0. Hence, is a rational number. (ix) is cube root of non-perfect cube. Hence, is an irrational number. (x) Here, is square root of a non-perfect square i.e. 6, thus it is an irrational number. The product of a non-zero rational number and an irrational number is always an irrational number. Hence, is an irrational number. (xi) is a repeating decimal. Thus, can be expressed as a fraction with an integer numerator and a non-zero integer denominator. Hence, is a rational number. (xii) 0.2022022220... is a non-terminating and non-repeating decimal. Hence, 0.2022022220... is an irrational number. (xiii) . 2 is rational number and is an irrational number. Since, on dividing a rational number by irrational number the solution is always an irrational number. Hence, is an irrational number. (xiv) can be expressed in the form of , where p and q are integers and q 0. Hence, is a rational number.

Mathematics

Classify the rational and irrational numbers from the following : (i) 5 (ii) 9/14 (iii) √3 (iv) π (v) 3.1416 (vi) √4 (vii) -√5 (viii) ∛8 (ix) ∛3 (x) 2√6 (xi) 0.36 (xii) 0.202202220... (xiii) 2/√3 (xiv) 22/7

Rational Irrational Nos

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