### Real Number System Class 9th Mathematics Term 3 Tamilnadu Board Solution

##### Question 1.Which one of the following is not a surd?A. B. C. D. Answer:As we knowsurd is a number in which we cant remove its square root(cube root …etc)A. = = 2 is not surdB. cant be simplified hence surdC. cannot be simplified hence surd cannot be simplified hence surdHence A is the answer.Question 2.The simplest form of isA. B. C. D. Answer:On simplification  = Hence B is the answerQuestion 3. is equal toA. B. C. D. Answer:On Simplification  = = Hence A is the answerQuestion 4. is equal toA. B. C. D. 2Answer:On rationalizing = =  Hence B is the answerQuestion 5.The rationlizing factor of isA. B. C. D. Answer:As we knowPrime factorization of 27 = 3  = = Hence C is the answerQuestion 6.Which one of the following is not true?A. is an irrational numberB. is an irrational numberC. 0.10110011100011110… is an irrational numberD. is an irrational numberAnswer:As we know an irrational number are those number which cannot be represented in a simple fractionA. √2 cannot be represent in simple fraction hence it is an irrational numberHence A is trueB. √17 cannot be represent in simple fraction hence it is an irrational numberHence B is trueC. 0.10110011100011110….cannot be represent in simple fraction hence it is a irrational number . Hence C is trueD. on simplification = Hence is rational number and not irrational.Hence D is the right answerQuestion 7.The order and radicand of the surd are respectivelyA. 8,12B. 12,8C. 16,12D. 12,16Answer:As we know here a is the order of surd and n is the radicand order = 8Radicand = 12A is the answerQuestion 8.The surd having radicand 9 and order 3 isA. B. C. D. Answer:As we know here a is the order of surd and n is the radicand Hence C is the optionQuestion 9. represents the pure surdA. B. C. D. Answer: Which is BHence B is the answerQuestion 10.Which one of the following is not true?A. is an irrational numberB. If a is a rational number and is an irrational numberC. Every surd is an irrational number.D. The square root of every positive integer is always irrationalAnswer:Option A is incorrect because √2 cannot be written in simple fraction.hence is irrational number, hence true.option B is incorrect as it can be written in simple form hence it is a rational numberAnd also √b cannot be written in simple form hence it is a irrational numberOption CAs we know surd is a number in which we cant remove its square root(cube root …etc) hence cannot represent, in simple fraction hence it is irrational numberHence C is trueOption DD is not true as square root of every positive integer is not always irrationalFor example, square root of 4 is 2 which is rational number hence D is not true.Hence D is the answerQuestion 11.Which one of the following is not true?A. When x is not a perfect square, is an irrational numberB. The index form of C. The radical form of D. Every real number is an irrational numberAnswer:As inOption AAs we know an irrational number are those number which cannot be represented in simple fractionHence they are not perfect squareFor example 3 is not a perfect squarealso is irrational numberhence A is trueoption Bindex form of number means power formas hence B is trueOption CRadical form means surd form Hence C is also trueOption DIt is not true that every real number is a rational numberFor example 2 is real number but not irrational numberHence D is not trueHence D is the right answerQuestion 12. is equal toA. 1B. 3C. 23D. 21Answer:using identity(a + b)(a-b) = a2 – b2 = = (5-4)= 1Hence A is the answer.

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