Show that each of the following is irrational : (i) (2 + √5)2 (ii) (3 - √3)2 (iii) (√5 + √3)2 (iv) 6/√3

Question

KnowledgeBoat · Accepted Answer

(i) Given, 9 is a rational number as it can be expressed in the form of , where p and q are integers and q 0. 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. 5. The product of a rational number and an irrational number is always irrational. i.e. The sum of a rational number and an irrational number is always irrational. i.e. Hence, is an irrational number. (ii) Given, 12 is a rational number as it can be expressed in the form of , where p and q are integers and q 0. 6 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 product of a rational number and an irrational number is always irrational. i.e. The difference between a rational number and an irrational number is always irrational. i.e. . Hence, is an irrational number. (iii) Given, 8 is a rational number as it can be expressed in the form of , where p and q are integers and q 0. 2 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. 15. The product of a rational number and an irrational number is always irrational. i.e. The sum of a rational number and an irrational number is always irrational. i.e. Hence, is an irrational number. (iv) Given, 6 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 division of a rational number and an irrational number is always irrational. i.e. Hence, is an irrational number.

Mathematics

Show that each of the following is irrational : (i) (2 + √5)2 (ii) (3 - √3)2 (iii) (√5 + √3)2 (iv) 6/√3

Rational Irrational Nos

Related Questions

Write down the examples of 4 distinct irrational numbers.