InterviewSolution
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InterviewSolution
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In the following equation, find which variables x, y, z etc. represent rational or irrational numbers:(i) x2 = 5(ii) y2 = 9(iii) z2 = 0.04(iv) u2 = 17/14(v) v2 = 3(vi) w2 = 27(vii) t2 = 0.4 |
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Answer» (i) x2 = 5 Taking square root both the sides, x = √5 √5 is not a perfect square root, so it is an irrational number. (ii) y2 = 9 y2 = 9 or y = 3 3 can be expressed in the form of p/q, such as 3/1, so it a rational number. (iii) z2 = 0.04 z2 = 0.04 Taking square root both the sides, we get z = 0.2 0.2 can be expressed in the form of p/q such as 2/10, so it is a rational number. (iv) u2 = 17/4 Taking square root both the sides, we get u = √17/2 We know that, quotient of an irrational and a rational number is irrational, therefore, u is an Irrational number. (v) v2 = 3 Taking square root both the sides, we get v = √3 Since, √3 is not a perfect square root, so v is irrational number. (vi) w2 = 27 Taking square root both the sides, we get w = 3√3 We know that, the product of a rational and irrational is an irrational number. Therefore, w is an irrational number. (vii) t2 = 0.4 Taking square root both the sides, we get t = √(4/10) t = 2/√10 We know that, quotient of a rational and an irrational number is irrational number. Therefore, t is an irrational number. |
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