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Identify the following as rational numbers. Give the decimal representation of rational numbers: (i)√4(ii) 3√18(iii) √1.44(iv) √9/ 27 (v) -√64 (vi) √100 |
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Answer» We have √4 = 2 =2/1 √4 can be written in the form of p/q, so it is a rational number. Its decimal representation is 2.0. We have, 3√18 = 3√2 x 3 x 3 = 3 x 3√2 = 9√2 Since, the product of a rations and an irrational is an irrational number. 9√2 is an irrational => 3 √18 is an irrational number. We have, √1.44 = √144/100 =12/10 =1.2 Every terminating decimal is a rational number, so 1.2 is a rational number. Its decimal representation is 1.2. We have, √9/27 = 3/√27 = 3/√3 x 3 x 3 =3/3√3 =1/√3 Quotient of a rational and an irrational number is irrational numbers so 1/√3 is an irrational number. =>√9/27 is an irrational number. We have, -√64 = -√8 x 8 = -8 = -8/1 -√ 64 can be expressed in the form of p/q ,so -√64 is a rotational number. Its decimal representation is -8.0. We have, √100=10 =10/1 √100 can be expressed in the form of p/q, so √100 is a rational number. The decimal representation of √100 is 10.0. |
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