EXERCISE Which of the following is irrational? (C) 7 (D) 81 (A) (B)
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1 EXERCISE Write the correct answer in each of the following:. Every rational number is a natural number an integer (C) a real number (D) a whole number. Between two rational numbers there is no rational number there is exactly one rational number (C) there are infinitely many rational numbers (D) there are only rational numbers and no irrational numbers. Decimal representation of a rational number cannot be terminating non-terminating (C) non-terminating repeating (D) non-terminating non-repeating 4. The product of any two irrational numbers is always an irrational number always a rational number (C) always an integer (D) sometimes rational, sometimes irrational 5. The decimal expansion of the number is a finite decimal.44 (C) non-terminating recurring (D) non-terminating non-recurring. Which of the following is irrational? 4 (C) 7 (D) 8 7. Which of the following is irrational? (C) 0.4 (D) A rational number between and is + (C).5 (D).8. The value of... in the form p q, where p and q are integers and q 0, is (C) (D) 0. + is equal to (C) (D) is equal to 5 5 (C) 5 (D) 0 5
2 . The number obtained on rationalising the denominator of 7 is (C) (D) is equal to ( ) + (C) (D) + 4. After rationalising the denominator of 7, we get the denominator as (C) 5 (D) 5 5. The value of is equal to (C) 4 (D) 8. If =.44, then + is equal to (C) 0.44 (D) equals (C) (D) 8. The product 4 equals (C) (D). Value of ( ) 4 8 is (C) (D) 8
3 0. Value of (5) 0. (5) 0.0 is 4 (C) 4 (D) 5.5. Which of the following is equal to x? x x ( ) 4 x (C) ( ) x (D) x 7 7 x EXERCISE. Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer.. Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.. State whether the following statements are true or false? Justify your answer. (i) is a rational number. There are infinitely many integers between any two integers. Number of rational numbers between 5 and 8 is finite. There are numbers which cannot be written in the form p q, q 0, p, q both are integers. The square of an irrational number is always rational. is not a rational number as and are not integers. 5 is written in the form p, q 0 and so it is a rational number. q 4. Classify the following numbers as rational or irrational with justification : (i) (viii) ( + 5 ) ( ) (x)
4 EXERCISE. Find which of the variables x, y, z and u represent rational numbers and which irrational numbers: (i) x = 5 y = z =.04. Find three rational numbers between (i) and 0. and 0. 7 u = 4 5 and 7 7 and 4 5. Insert a rational number and an irrational number between the following : (i) and 0 and 0. and and and 0. and.57 and. (viii).000 and.00. and (x).758 and Express the following in the form p q, where p and q are integers and q 0 : (i) (viii)
5 5. Simplify the following: (i) ( ) (viii) + 8. Rationalise the denominator of the following: (i) (viii) Find the values of a and b in each of the following: (i) 5+ = a = a = b = a + 5b If a = +, then find the value of a a.. Rationalise the denominator in each of the following and hence evaluate by taking =.44, =.7 and 5 =. (i) upto three places of decimal Simplify : (i) ( ) ( 5)
6 EXERCISE 4. Express in the form p q, where p and q are integers and q 0.. Simplify : If =.44, =.7, then find the value of 4. If a = If x = and y =. Simplify : ( ) ( ) 4 5, then find the value of a +. a , then find the value of x + y Find the value of ( ) ( 5 ) ( 4 ) 4 5
7 ANSWERS EXERCISE. (C). (C). (D) 4. (D) 5. (D). (C) 7. (D) 8. (C). (C) 0. (C)... (D) (C) 7. (C) (C) EXERCISE. Yes. Let x =, y = be a rational number. Now x + y = + = = Which is non-terminating and non-recurring. Hence x + y is irrational.. No. 0 = 0 which is not irrational.. (i) False. Although is of the form p q but here p, i.e., is not an integer. False. Between and, there is no integer. False, because between any two rational numbers we can find infinitely many rational numbers. True. is of the form p q but p and q here are not integers. False, as ( 4 ) = which is not a rational number. False, because False, because = 4 = which is a rational number = = which is p, i.e., 5 is not an integer.
8 4. (i) Rational, as = 4 8 =, which is the product of a rational and an irrational number and so an irrational number. =, which is the quotient of a rational and an irrational number and so an irrational number =, which is a rational number. 7 Irrational, 0.4 =, which is the quotient of a rational and an irrational =, which is a rational number. 7 Rational, as decimal expansion is terminating. (viii) ( + 5) ( ) =, which is a rational number. (x) Rational, as decimal expansion is non-terminating recurring. Irrational, as decimal expansion is non-terminating non-recurring. EXERCISE. Rational numbers:, Irrational numbers: (i),. (i).,.,. 0.0, 0.0, ,, ,, (i)., , ,... 5, , , , , (viii) 0.000, , (x).75, (i) (viii) 40
9 5. (i) (viii) 5 4 (i) (viii) (i) a = a = 5 b = a = 0, b = 8.. (i) (i) EXERCISE
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