Saved Bookmarks
| 1. |
In the following equations, find which variables x, y, z etc. represent rational or irrational numbers: (i) x2 = 5 (ii) y2 = 9 (iii) z2 = 0.04 (iv) u2 = 17/ 4(v) v2 = 3 (vi) w2 = 27 vii) t2 = 0.4 |
|
Answer» (i) We have x2 = 5 Taking square root on both sides. => √x2 = √5 => x = √5 √5 is not a perfect square root, so it is an irrational number. (ii) We have y2 = 9 => y = √9 =3 =3/1 √9 can be expressed in the form of p/q, so it a rational number. (iii) We have z2 = 0.04 Taking square root on both sides, we get, √z2 =√0.04 => z = √0.04 = 0.2 = 2/10 = 1/5 z can be expressed in the form of p/q, so it is a rational number. (iv) We have u2 =17/4 Taking square root on both sides, we get, √u2 =√17/4 => u = √17/2 Quotient of an irrational and a rational number is irrational, so u is an irrational number. (v) We have v2 = 3 Taking square root on both sides, we get, √v2 = √13 => v = √3 √3 is not a perfect square root, so y is an irrational number. (vi) We have w2 = 27 Taking square root on both sides, we get, √w2 = √27 => w = √3 x 3 x 3 =3√3 Product of a rational and an irrational is irrational number, so w is an irrational number. (vii) We have t2 = 0.4 Taking square root on both sides, we get √t2 = √0.4 => t = √4/10 = 2/√10 Since, quotient of a rational and an irrational number is irrational number, so t is an irrational number. |
|