PROVING IRRATIONALITY OF NUMBERS REAL NUMBERS 01 Class 10th Mathematics (Practice Sheet) 1 Which of the following statements about irrational numbers is true? A. Irrational numbers can be expressed as ratios of integers. B. The decimal expansion of an irrational number is always terminating. C. The addition of an irrational number and a rational number results in a rational number. D. Irrational numbers are always closed under multiplication. 2 If p divides a2 , then according to the given theorem, what can be concluded? A. p divides a B. a divides p C. p divides b D. p divides b 3 Which of the following is an example of an irrational number? A. 2 3 B. √4 C. π D. 0.5 4 What is the result of the multiplication of two irrational numbers? A. Always irrational B. Always rational C. Can be either rational or irrational D. Neither rational nor irrational 5 Which of the following is an irrational number? A. √25 B. √16 C. √10 D. √9 6 Prove that 3 + 2√5 is irrational. 7 Given that √2 is irrational, prove that (5 + 3√2) is an irrational number. 8 Prove that 1 √2 is an irrational number. 9 Which of the following are Rational Numbers or Irrational Numbers? 2, −.45678 ... , 6.5, √3, √2 10 Find two irrational numbers lying between √2 and √3. Page 1 Email: Phone No: Website:
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